NO· 141

GOVERNMENT OF WEST PAKISTAN
HIGHA!AY

DEPARTMENT

/

LAHORE

CODE OF PRACTICE
HIGHWAY BRIDGES

1967

SAEED AHMAD,...
Tl1e purpose or tlLtn <,;Jd~.l ot ?ra.c~:ic,L "1.:; to e.stabl:.sh
tnini1nun1 standards and 'l'DLic:i r: p.:cc::;d,Jres En...
CONTENTS

Article
SECTION 1 - GENERAl, FEATURES OF DESIGN
1.1
L2
L3
1.4
1.5

1.6
1.7
L8
L9
l, 10
1.11
1.12
1.13
1.14
1.15
...
Article
SEC'!'ION 3 3o 1,

DISTRIBU'I'IO:~

U? LOAI;S

Distribution of Wheel Loads to Stringers,

Lcr:git:.~dL1ai

Beams a...
Article

7.10
7.11

7.12
7.13
7.14
7.15

7.16
7.17
7.18
7.19

Ultimate Flexural Strength
Maximum and Minimum Steel Percent...
SECTION l - GENERAL
l l
<

FEA1~RES

OF DESIGN

PRELl NI ;lARY DATA

The following information <,.;ill normallJ' be requir...
(b)

The approximate outlines of the banks, the high water
channel(if different from the banks), and the lmv water
channel...
(d)

(e)

The low water level;

(f)

The ordinary Flood level;

(g)

The highest flood h:vel and the yo::,ars in which it ...
(g)

The possibility of subsequent changes in the catchment
like afforestation, deforestation, urban development,
extent o...
at intervals 1000 ft. apart in straight reaches and 500 ft.
apart along curves for proper representation on the model.
The...
'(A)
The maximum discharge >-Ihich the stream crossing or culvert shall be
designed to pass shall be determined by a consi...
0.020 for ea.rth in good order and regimen~ free
from stones and weeds
0.025 for· earth in fair order and regimen, free

n...
The vetted perimeter thus obtained for a straight reach of the stream
is very nearly the effective width of waterway in su...
of the deck structure inclusive of main girders in the central
half of the clear opening.
(b)

(c)

,.

1

"1_,.-.

~.

J
...
when dealing with natural streams in alluvial beds:
For regime conditions in a stable channel
1/3
d = 0.473(+)
For restric...
(3)

at noses of piers

2.0 d

(4)

at upstream noses of guide
banks

2.5 d

Due allowance shall be made for a::.1 increas...
r------ ·---------- 1
HORIZONT.D..L CLElf.<ANCE

~·--------------~-----,--~--------~=------1

'

MINIMUM ROADWAY WIDTH

:T...
abutments supporting other types of superstructure. The foundations
shall in all cases be taken down to a depth vhich will...
1.13~

CURBS AND SAFETY CURBS

The face of the roadway curb is defined as the battered or sloping
surface on the roadway s...
The height of traffic railing shall be not less than 2'-3" measured
from the top of the roadway, or curb, to the top of th...
1. 1 :J-

ROADWAY WIDTH, CURBS A~1D CLEARANCES FOR TUNNELS
(See Figure 2.)

(A) Roadway Tidth - The clear width bet,Jeen c...
F()tD!.1.Y
t~)"j"

CLEARANCE
T~NO

LA

v~rlO-TH

LESS

YTi'-~i~.Pi

.t'U11l FOR UNDER
HIGHW.LW TRAFFiC

FIGURE 3

1. 20-

...
l.

21~

ROAmJAY

WIDTH~

CURBS AND CLEARANCE FOR DEPRESSED ROADWAYS

(A) Roadway Width-~ The clear vidth between curbs sh...
SECTION 2 - LOADS
2.1 -

LOADS

Structures shall be proportioned for the following loads and forces
when they exist:
1.
2....
Materials

Lbs./Cu.Ft.

6. Cement Concrete,reinforced
7. Earth (Compacted)
8. Macadam (binder premix)
9, Rolled Steel
10. ...
C.

SHEAR IN SLABS

The maximum shear in the top and bottom slabs shall be assumed
to occur at a distance out from the fac...
10'-0"

65~~

10'-0"

15,000

15,000

Lbs.

__

Lbs.

15POO
Lbs.

6,000 6,000
Lbs.
Lbs.

~~

·---N

•
.f"-

~---]

:;-----...
of vehicles shall be considered as acting simultaneously in a
position causing maximum stresses.
(3)
Vehicles in adjacent ...
2. 8-

SIDEWALK, CURB, SAFETY CURB AND RAILING LOADING

A.

Sidewalk Loading

Sidewalk floors, stringers, and their immedi...
to the lmver railing shall not exceed 200 pounds. If there is no
lower rail, the web members shall be designed to resist a...
I
1

impact fraction (maximum 30 per cent)
length of span in feet

For uniformity of application the span length "V' shall...
types of bearing:
For roller bearings
0.03
For sliding bearings of hard copper alloy
0.15
For sliding bearings of steel on...
(B)

Substructure Design

Forces transmitted to the substructure by the superstructnr-2 and
forces applied directly to the...
lengths of 125 feet, the following wind loading may be used in lieu
of the more precise loading specified above.
W ( wind ...
The range of temperature shall generally be as follow
Metal Structures
Moderate climate from.0°to 120°F
Extreme climate fr...
the pier extending above the point of deepest scour.
piles when a pile foundation is used.

This will include

(D)
When th...
2.17-

EARTHQUAKE STRESSES

In regions where earthquakes may be anticipated, provlslon shall be
made to accommodate latera...
Section 3 - DISTRIBUTION OF LOADS
3.1-

DISTRIBUTION OF HHEEL LOADS TC STRINGERS, I.DNGITUDINAL BEAHS
AND FLCC'"R 3EAHS

(...
Notes:
S
(a)

Design of I=Beam Eridge by N.M. Newmark-Proceedings,
ASCE, March 1948.

(b)

In this case the load on each s...
(C)

Bending Moment

Bending moment per foot ~·7id~h
methods given under Cases A and H.

o[

sJab shall be calculated acco...
(Impact not included)
For simple spans up to 35'
Use N == 0.9S

K

X

For simple spans 35' to 70'
Use H = (1.35
(D)

c

.....
(F)

Shear and Bond stress in Slabs

Slabs desi~ned for benrlin~ moment in accordance with the foregoing
shall be consider...
(I)

Slab Supported on Four Sides

In the case of slabs supported alo~:tg four edge;o. and reinforced in both
directions t...
Section 4- l-'l.ILITARY LOADING
4.1-

LOADING

1':'1e military loading on the roadways of bridges or incidental
structures...
HORIZONTAL CLEARANCE
The minimum clearance betweec-1 th2 rc.advn:;.y i;:;.ce o"" ctcrb and the
outer edge of ch2. track sh...
(C)

Bending Moment

B..::r::ding moment per foot of -;,d.d::J·; or s:c;.b sha.lJ. be
according to methods give.n nnder Ca...
Section 5 -· UNIT STRESSES
5.1

GENERAL

Unless otherwise noted the allowable unit stresses indicated herein
are given in ...
5.2-

CONCRETE STRESSEs(i)

(A)

Standard Notations and Assumptions
fc

=

Permissible Extreme fiber stress in compression...
(2)

Shear
Cube
Strength
Beams without web reinforcement
Longitudinal bars not anchored
or plain concrete footings----

0....
SECTION 6 - CONCRETE DESIGN
6.1-

GENERAL ASSUMPTIONS

The design of reinforced concrete members under these specification...
(8)
For the determination of external reactions, moments, shears,
and deflections, moments of inertia of rigid frame and c...
In continuous bridges, prov~s~ons shall be made in the design to
resist thermal stresses induced or means shall be provide...
(E)

Construction Joints

When a construction joint is required between the slab and the seem
of the beam, the shear-keys ...
be extended at the supports and at other points between the supports
as indicated in (2) to (5) below. These paragraphs re...
8 bars full length of the girders may be used
( ")
n

Reinforcement of Beam Sides

The depth of the beam between the main ...
(measured in a direction parallel to that of the
main reinforcement), or the total of all bars bent
up in any one plane.
b...
V'

A

f

v

sino(

1be bond between concrete and reinforcing bars in beams and slabs
shall be computed by the following f...
embedment of the requisite length in the upper or lower half of the beam
provided at least one half of such embedment is a...
The least lateral dimension of a column shall be taken as: (1) for rectangular
columns, the over-all thickness along a pri...
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
Pakistan Building Code 1967
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Transcript of "Pakistan Building Code 1967"

  1. 1. NO· 141 GOVERNMENT OF WEST PAKISTAN HIGHA!AY DEPARTMENT / LAHORE CODE OF PRACTICE HIGHWAY BRIDGES 1967 SAEED AHMAD, T.Pk., P.S.E.-1 DIRECTOR GENERAL-HIGHWAYS HOWARD, NEEDLES, TAMMEN & BERGENDOFF, INT. INC. GENERAL HIGHWAY CONSULTANTS
  2. 2. Tl1e purpose or tlLtn <,;Jd~.l ot ?ra.c~:ic,L "1.:; to e.stabl:.sh tnini1nun1 standards and 'l'DLic:i r: p.:cc::;d,Jres End p~e.cti<:efl for the des:Lgr: ot' us!.1al ~ c.f 1tigtr~va:.r struct:.:.:...~~s :_n th.e Province of West Pak1stan. T~·~au~h s~ch st~sdarJization of methods, a Tnuch greater be realized in design With this in mind this first ~ditlon of th2 r~de hs~ b~en written co cover pr i.mc;.r t reinforced and ~r~strsssed conc=~te design Referenc.e has. be.er1 tnade to th"E.~ :s·l_-it·!.sh l-;t~::..r:.dard Spec.ific;:rtions for those special cases vit-1~:re ~:t2;:::1 desLgn ~~~ill be required. ex pet iei:JCe and the iutu_rs c_~.;s.i.l~.:;-~) Ll.i ty of more econou1ical and different structural mate~ials wiLl dictate the necessity that this Cod2 be revised pericdtcally. It is expected that all those respo.nsibl0 fer ::otructm:e designs 1<vi1l be alert to the need for such revisions. Suggestions for updating the Code along these lim':s are encouraged.
  3. 3. CONTENTS Article SECTION 1 - GENERAl, FEATURES OF DESIGN 1.1 L2 L3 1.4 1.5 1.6 1.7 L8 L9 l, 10 1.11 1.12 1.13 1.14 1.15 1.16 1.17 1.18 1.19 1,20 L21 Preliminary Data Determination of Waterway Area Spacing and Location of Piers and Abutments Vertical Clearances Restricted Waterways Obstruction and River Training Determination of the Haximum Depth of Scour Depth of Foundations Size of Culverts Openings Length of Culverts Width of Roadway and SidewalL Clearances Curbs & Safety Curbs. Railings Roadway Drainage Supereleva.tion Floor Surfaces Utilities Roadway Width, Curbs and Clearance for Tunnels. Roadway Width, Curbs and Clearance for Underpasses (undivided Highways) Roadway Width, Curbs and Clearances for depressed Roadway 1-l 1-5 1-8 1-8 1-9 1-9 1-9 1-11 1-13 1-13 1-13 1-13 1-14 1-14 l-15 1-15 l-15 1-15 1-16 1-17 1-18 SECTION 2 - LOADS 2.1. 2,2 2,3 2.4 2.5 2.6 2.7 2.8 2 ,.9 2.10 2 011 2.12 2.13 2.14 2.15 2,16 2.,17 2.18 T oads ... Dead Load Live Load Highway Loadings Standard Truck-Train Loading Application of Loadings Reduction in Load Intensity Sidewalk, Curb, Safety Curb and Railing Loading Impact Longitudinal Forces Wind Loads Thermal Forces Uplift Force of Stream Current Buoyancy Earth Pressure Earthquake Stresses Centrifugal Forces i 2-1 2-1 2-3 2-3 2-3 2-5 2-5 2-6 2-7 2-8 2-9 2-11 2-12 2-12 2-13 2-13 2-14 2-14
  4. 4. Article SEC'!'ION 3 3o 1, DISTRIBU'I'IO:~ U? LOAI;S Distribution of Wheel Loads to Stringers, Lcr:git:.~dL1ai Beams and Floor Beams Distribatic.n of Loads and Design ot Cor:crete Slabs Distribution of Wheel Loads through Earth Fills 3-1 3-2 3-6 SECTION 4 - HILITARY l.0ADING 4.1 Loading 4.2 Horizontal Clearance Distribr;tion of Load to 1.-o::gitudinal Stringsrs Impact Distribat io:.~ cf Loads and Dt:'.s ig-;:1 of Concret<.:>. Slabs 4.3 4.4 4,,5 !.; -1 4-2 4-2 SECTIO"N 5 - illiiT STRESSES 5.1 5.2 General Concrete Stresses 5 .. 3 ReinforcP.ment 5.4 Steel Stressr.:s 5-l 5-2 5-3 5-3 SECTION 6 - CONCRETE DESIGN 6-1 6-2 6. 3 Ge;:1eral Assumptions Span Lengths Expansion 6.4 T-Bea.ms 6-3 6.5 6.6 6.7 Reinforcement Compression Reinforcement Web Reinforcement Columns Concrete Arches Viaduct Bents and Towers Box Girders 6.8 6.9 6.10 6.11 c. " u-L 6··4 L:'t B<::ams 6-6 6-6 6-9 6-16 6-17 6-18 SECTION 7 - PRESTRESSED CONCRETE 7.1 7.2 7.3 7 o4 7oS 7.6 7.7 7 .. 8 7.9 7-1 7-1 7-3 7-3 7-3 General Notation Design Theory Basic Assumptions Loading Stages Load Factors Allowable Stresses Loss of Prestress Flexure 7-4 7-4 7-5 7-7 ii
  5. 5. Article 7.10 7.11 7.12 7.13 7.14 7.15 7.16 7.17 7.18 7.19 Ultimate Flexural Strength Maximum and Minimum Steel Percentage · Nonprestressed Reinforcement Shear Composite Structures End Zone of Concrete I-Beams Cover and Spacing of Prestressing Steel Embedment of Prestressing Strand Concrete Strength at Stress Transfer Reinforcement in Beams 7-7 7-9 7-9 7-10 7-11 7-12 7-12 7-13 7-13 7-13 SECTION 8 - PILE LOADS AND BEARING POWER OF SOILS 8.1 8.2 8.3 Bearing Power of Foundation Soils Angles of Repose Bearing Value of Piling SECTION 9 - 9.1 9.2 9.3 9.4 9.5 SUBSTRUCTL~ES 8-1 8-1 8-2 & RETAINING WALLS Piles Footings Abutments Retaining Walls Piers 9-1 9-4 9-7 9-8 9-9 SECTION 10 - STEEL DESIGN 10.1 Design and Construction 10-1 iii
  6. 6. SECTION l - GENERAL l l < FEA1~RES OF DESIGN PRELl NI ;lARY DATA The following information <,.;ill normallJ' be required for the proper design of structur2s. A. STREAM (]) CROSStNG~ An 1ndex map to a suitable smdll scale ltopo she~ts scale one i Pch to one mile would do ir. most cases) showing the proposed locat ton of the bridge, the alternative :.;i.tes investigated and rejected, the ex·i_st ing comm•1nicat ions, the general topography of the country, and the important towns, etc., in the 'Jicinity. [ contour survey plan of the stream showing all topographical fentures extending to the distance shown below(or such other greater distances as the engineer restonsible for the design may direct) upstream and dmvnstream of any of the preposed sites ar,d to a sufficient distance on either side to give a clear indication of topographical or OT:her features that might influence the location and design of the bridge and its a~proaches. All sites for crossings worth consideration shall be shown on the plan. {2) (a) 300 feet for catchment area less than one square mile (scale not less than one inch to 100 feet). (b) 1000 feet for catchment areas of 5 square miles (scale not less than one inch to 100 feet). (c) One mile for catchment areas of more than 5 square miles (Scale not less than one inch to 330 feet). Note:- In djfficult country and for crossings over artificial channels the engineer responsible for the design may permit discretion to be used regarding the3e limits of distance,provided that the plans give sufficient information on the course of the stream and the topographical features near the bridge site. (3) A site plan to a suitable scale showing details of the site selected and extending not les(:> than 300 feet upstream and downstream from the centre line of the crossing and covering the approaches to a sufficient distance which in the case of a large bridge shall be not less than a quarter of a mile on either side of the stream. The plan shall include all information that is essential for complete and proper appreciation of the project. The normal requirements are given below; (a) The name of the stream or bridge and of the road and the identification number allotted to the crossing; 1-1
  7. 7. (b) The approximate outlines of the banks, the high water channel(if different from the banks), and the lmv water channels with contours at suitable level intervals in the bed anJ beyond the banks and the line of the deepest points along the dry weather channel; (c) The direction of flow of 1vater at maximum discharge end if possible, the extent of deviation at lc~er discharge; (d) The alignment of existing approaches and of the proposed crossing and its approache,s; (e) The angle and direction of sk2w if the crossing is aligned on a skew; (f) The name of the nearest inha:).Lu"d identifiable locality at either end of the crossing on the roads leading to the site; (g) References to the position(vir:h description ar.d reduced level) of the bench mark used as datum; (h) The lines and identificatiou numbers of the crosssec::ions and logitudinal section taken Hith!_n the scope of the site plan, and the exact location of their extreme points, (i) The locations of trial pits or borings each being gh'en an identification number; (j) The location of all nullahs, buildings, wells, outcrops of rocks, and other possible obstructions to a road alignment. (4) A cross-section of the stream at the site of the proposed crossing ( Scale not less than one inch to 100 feet horizontally , exaggerated vertically to a scale of not less than one inch to 10 feet) and indicating the following information: (a) The name of the stream and the serial number allotted to the crossing; (b) The name of the road with mileage and chainage of the centre of the crossing; (c) The bed line up to the top of the banks and the ground line to a sufficient distance beyond the edges of the stream, with levels at intervals sufficiently close to give a clear outline of markedly uneven features of the bed or ground showing right and left bank and names of villages on each side; 1-2
  8. 8. (d) (e) The low water level; (f) The ordinary Flood level; (g) The highest flood h:vel and the yo::,ars in which it occur, red. State iE the flood level is affected by back-water and if so, give details; (h) The catchment area, maximum discharge specified in Article 1.:2(A.) arvl correspo~1ding average velocitiJ a:: tbe site of the crossi~g; (i.) (5) The nature of the surface soil in bed, banks and approa, ches, with trial pit or bore hole sect ion.s showing the levels and nature of the various strata down to hard strata suitable for foundation and the safe intensity ot pressure on the foundation soil; (as far as practicable, the spacing of trial pits or bore holes should be such as to provide a full description of all substrata layers along the vl:ole lengt.b and >,vidth of the crossing); The estimated depth of sco:.;r oc, if the scour depth has been observed, the depth of scour, with details of obstructions or of any other special causes responsible for the scour. - lo·;-·J_gitudinal ~:;ection of the strecr~n snov11Eg tbt .site oj the bridge with the highest flood lev2l, the ordiGary flood level, the low water level, and the bed levels at suitably spaced intervals along the approximate centre line of the deep water cha~nel between the extreme p~.dnts ~-:; vhich the survey map required in Article 1.1A(2) e:ztends, The horizontal scah' not let=:s than one inch to 100 f.efi!t. {6) A note givi:~.g as iar as possible ti;e following particulars relating to the catchment area; (a) Jbe size of the catchment; (:;) The shape (c) The intensity and frequency of rai.nfall in the catchment; (d} The slope of the catchment, both longitudinal and transverse; (e) The nature of the catchment, whether under forests, under cultivation, urban etc; (f) The nature of the soil crust, porous or rocky, etc; or the catchment;
  9. 9. (g) The possibility of subsequent changes in the catchment like afforestation, deforestation, urban development, extent of reduction in cultivated area, etc; (h) Storage in the catchment artificial or natural. (7) A chart of the periods of high flood levels for as many years as the relevant data are recorded. (8) A note giving important details of the bridges, i f any, crossing the same river within a reasonable dist:auce oE the proposed bridge. (9) The minimum permissible vertical ch~Hl!le:l clearar:ce and the b<1sis on which it has been determined mentioning any special requireme<lts for navigation. (10) Liability of the site of earthquake disturbances. (11) A brief description of the reasons for selection of the particular site for the crossing accompanied, if necessary , '"ith typical crosf"= section of the stream at suitable alternative crossing places both upstream and downstream of the selected site. (12) Sub-soil data of the stream at the site of the bridge should obtained at four or more points in the cross section. (13) te All other pertinent information affecting the design such as: (a) (b) (c) (d) (e) (f) (g) (h) Width of roadway curb to curb Vertical and horizontal a~ignment Cross Slopes Live Load to be applied Safety Curb, footpatb and/or animal path Utilities to be carried by the superstructure Location and type of piers and foundations Freeboard Clearance (14) In case of streams having discharge over 50,000 cusecs, the hydraulic design should be checked by model studies. The following data shall be required. (a) A site plan showing the location of the bridge with respect to the stream. A stretch at least 5 miles up stream and 3 miles down stream or two 'S' curves up stream and one 'S' curve down stream of bridge, whichever is longer, should be given on the plan. In order to indicate its dominent course, the course"·Of the river or stream over a five (5) years period should be shown. (b) The cross sections of the stream should be observed 1-4
  10. 10. at intervals 1000 ft. apart in straight reaches and 500 ft. apart along curves for proper representation on the model. The location of all cross sections should be marked on the site plan. (c) Gauge discharge curves and hydrograph of the stream at the bridge site should be collected for the last 5 to 10 years. If such data is not ave.ilable, data pertaining to the hydrographs and guage discharge of the rr;_ain stream, up stream and down stream of the site may be used. B. H1GHI-IA'f AND RAILROAD CROSSINGS (1) An index map to a suitable small scale (topo sheets scale one iw_h to one mile wou.ld do in most cases) shmving the proposed location of tht.: bridge, t:he exist5_ng communications, the important towns etc., in the vicinity. (2) A plan and elevation of the proposed bridge showing span lengths; critical vertical clearance of superstructure required above roadway or railroad; critical horizontal clearance to piers and abutments; depth of structure hom profile grade to bottom of grider; location and number of bore holeL;;; and the profile of the bridge and its approaches. (3) A cross section of the proposed bridge showing the number, £ype and spacing of girders; the thickness of slab; the cross slope; width ,-,f roadway curb to curb; the width of <>afety walk, footpath and/or animal path, and the utilities to be carried by the superstructure. (4) A profile of the highway or railroad. (5) A cross section of the highway or railroad. (6) Type of pier to be used. (7) Type of footing to be used, whether rock bearing, soil bearing or pile bearing and the allowable capacities of each. (8) 1. 2- Live load to be applied. DETERMINATION OF WATERWAY AREA For the determination of the vaten1ay area UJ. be provided for a stream crossing or culvert, a careful study shall be made of local conditions, including flood height, flov;r and frequency, size and performance of other openings in the vicinitY carrying the same stream, characteristics of the channel and of the watershed area, available rainfall records and any other information pertinent to the problem and likely to affect the safety 'or economy of the structure. l-5
  11. 11. '(A) The maximum discharge >-Ihich the stream crossing or culvert shall be designed to pass shall be determined by a consideration of the following methods: (1) From the rainfall and other characteristics of the catchment which together from the general formula; Q = c n X A Where Q is the maximum flood discharge in cubic feet per second (cusecs), A is the area of catchment of the stream in square miles, 11 n 11 an exponent varying from 0.5 to 1.0, and C a varying coefficient depending upon the characteristics of the terrain. Some typical formulas are: (a) Dicken's formula Q = c 3/4 X A Where C is equal to 750 for mountainous areas and 500 for planes (b) Ryves formula Q = c X A213 Where C is equal to 500 for mountainous area and 350 for planes. (C) Inglis formula 7000 A Q (d) VA+ 4 M.E.S. formula Q = 2100 X 1/2 A (2) From the hydraulic characteristics of the stream such as the cross-sectional area, and slope of the stream allowing for velocity of flm.;r. In this method the velocity is obtained from the formula 1.486 2/3 1/2 V = X r X S n Where r = hydraulic mean depth in feet S Slope V mean velocity in feet per second n coefficient of rugosity of stream bed 1-6
  12. 12. 0.020 for ea.rth in good order and regimen~ free from stones and weeds 0.025 for· earth in fair order and regimen, free n from stones and weeds 0.030 for earth in bad order, with occasional stones and weeds 0.035 for streams in bad order and. regimen with stones and weeds 0.050 for torrential rivers in beds covered with detritus and boulders. The velocity thus obtained is then multiplied by the crosssectional area to give the required discharge Q. (3) From the Unit Hydrograph method The results from the above methods should then be compared and with proper judgement, arrive .. at the design discharge to be used. (B) Having arrived at an estimate of required discharge either by the calculations from the preceding sections or by flood data secured fro1n ~vailable reports of gauging stations or local high water marks, the next step is to design an opening that ·will pass this amount of water without damage to the Btructure or to adjacent work or properties. (1) For artificial irrigation, navigation, and drainage channels, the effect~ve width of waterway shall generally be equal to the width of channel at mid~depth, but concurrence shall be obtained invariably from the authority controlling the channel. If it is proposed to flume the channel at the site of the bridge, the flurning shall be subject to the consent of the same authority and in accordance with its essential requirements. (2.) For nonmeandering natural streams not widE. than 100 feet in alluvial beds but with well-defined banks and for all natural channels in beds with rigid inerodible boundries, the width of waten1ay shall be the distance between banks at that water ;.;ul·face elevation at which the designed discharg~ was determined. (3) For large natural streams in alluvial beds and having undefined banks, the width of waterway shall be determined from the design discharge, using some accepted rational formula such as Lacey's formula for a regime flow condition where p = 2.67 Q 1/2 P being the wetted perimeter in feet, and Q the discharge in cusecs of a stream consisting of alluvial beds like sand, or clay, transported and deposited by flowing water. 1-7
  13. 13. The vetted perimeter thus obtained for a straight reach of the stream is very nearly the effective width of waterway in such cases. SPACING AND LOCATION OF PIERS AND ABUTMENTS The following consideration shall govern the spacing and location of .nd abutments: (a) Piers and abutments shall be so located as to make the best use of the foundation conditions available. (b) Subject to (a) above, the suitable economical span shall be adopted, modified, if necessary, to suit navigational and aesthetic requirements. The number of piers should be limited as much as is practicable, they catch debris and thus the effective waterway could be reduced substantially. (c) The alignment of piers and abutments shall, as far as possible, be parallel to the mean direction of flmv in the stream but provision shall be made against harmful effects on the stability of the bridge structure and on the maintenance of adjacent stream banks caused by any temporary variations in the direction and velocity of the stream current. VERTICAL CLEARANCES Clearance shall be allowed according to navigational or anti:tion requirements or, where these condition do not arise, ordinarily .OWS: (a) For o1~enings of high level bridges, which are approximately rectangular, or with a very flat curve of the soffit of super-structure, as for instance in the case of beam, frame, or bowstring superstructures, continuous girders or open spandral arches •vith suspended decking, the minimum clearance shall be in accordance with the following table: DISCHARGE MINIMUM VERTICAL CLEARANCE Below 10 cusecs 10-100 cusecs 101-1000 cusecs 1001-10,000 cusecs 10,001-100,000 cusecs Over 100,000 cusecs Ft. 0 1 2 In. 6 6 0 3 4 0 5 0 0 The minimum clearance shall be measured from the lowest point 1-8
  14. 14. of the deck structure inclusive of main girders in the central half of the clear opening. (b) (c) ,. 1 "1_,.-. ~. J In structures provided '>vith metallic bearings such vertical clearance shall be allowed as will ~revent the submergence of those bearings. In the case of artificial channels, e.g., irrigation canals having controlled flov-1 and carrying no floating debris, the Engineer~in·Charge may at his discretion provide less vertical clearance than that specified in sub-clauses (a) and (b) above. RESTRICTED WATERWAYS When it is necessary to restrict the waterway to such an extent that the resultant afflux will cause the stream to discharge at erosive velocities, protection agains~ damage by scour shall be afforded by deep foundations, C'J.rtain or cut·"off walls~ rip-rap, bearing piles, or other euitable means" Likewise embankment slopes adjacent to a 11 structures subject to erosion nhall be adequately protected by pitching, revetment walls or other suitable const-ruction. 1. 6- OBSTRUCTION AND RIVER TRAINING Obstructions in the river bed likely to divert the current or c3use undue disturbed flow or scour and thereby endanger the safety of the bridge shall be r:::mov('.'d as far as practicable for some distance upstream and down~ stream of the bridge depending on the river characteristics. Attention shall be given to river training and pro tee tion of banks over such lengths of the river as require it. L /c DETERMINATION OF THE MAXIMUM DEPTH OF SCOUR (A) The maximum depth of scour in a stream shall be ascertained whenever possible, by actual soundings at or near the site proposed for Lhe bridge, during a flood before the. scour holes have had time to silt up appreciably. Due allowance shall be made in the observed depth for increase in scour resulting from (1) The design discharge being greater than the flood discharge during which the scour was observed; (2) The increase in velocity due to the obstruction in flow caused by construction of the bridge. (B) Where the practical method of determining scour described at(A) above is not possible, the following emperical approach may be used as guide
  15. 15. when dealing with natural streams in alluvial beds: For regime conditions in a stable channel 1/3 d = 0.473(+) For restricted flow d = k 0.9 ( q2 )1/3 f d Normal depth of scour below H.F.L.(high flood level) Q Total design discharge in cusecs q Design discharge per foot of width in cusecs k A factor varying conditions. For to be used shall Directors of the f Lacy's silt factor for a representative sample of the bed material. The silt factor is' approximately equal to 1. 76 m% where m is the wetted mean diameter in milimeters (rnm) of the bed material. See table for value of f given by Lacy for various grades of bed material from 1 to 3 derending on local a major stream crossing the factor be decided on consultation with the Bridge and Research Directorates. LACY'S SILT FACTOR l1aterial f Medium silt, canges canal distributary Standard silt, Punjab data Medium sand Coarse sand Fine Bajri and sand Heavy sand Coarse Bajri and sand Coarse gravel Gravel and bajri Boulders and Gravel 00.233 00.323 00.505 00.725 00.988 01.290 02.420 07.280 26.100 50.100 00.850 01. 000 01.250 01.500 01. 7 50 02.000 02.750 04.750 09.000 12.000 The maximum depth of scour shall be taken as follows: (1) In a straight reach 1. 5 d (2) at a right angle bend 2. 0 d 1-10
  16. 16. (3) at noses of piers 2.0 d (4) at upstream noses of guide banks 2.5 d Due allowance shall be made for a::.1 increase in concentration through a portion of the waterway. of flovJ -There the computed depth of scour ceachss 'AI'"ll into layers, as iadicated by boring informatior;, oi: relatively scour free material (i, e, gravel and boulders) the computed depth of scour may be red1.<ced. 1. of 8~ ~he DEPTH Of FOUNDll'IONS (A) The depth of foundations shall be d~termi:J.ed by consideration safe hearing capacity of th~ soil after taking into account the effect of sco-ur., (B) In all doubtful cases, the bearing capacity of the foundation shall be determined by actual loading tests. The adequate th.ickne133 cf the foundation bearing layer of the soil shall be ascertained by borings o:r trial pits . ,oni} l'he maxirnum toe pressure o:n the foundatir:;r. bearing l"l.y~r ~vorst: cornb:l~~1ati.on. of dir£,_ct forc2s a::td ov·ert:jrilirtg mo1nex.1~.s :~hn11 h<.; cB.lcuJat!"d f:or each individt:al fouadaticn. In calcul'l'::ing this prcssure 1 the. (~ffect of passi,/e. rr-.::~i.stance of the earth of t.~he. sides of th~) foundation structure. ,nay be taken h:to Hcco:.mt be low the ma;...:1mum depth of the scour only The effect of skin friction on the sides of the foundation :;tructure may be ignored normally except in the ca~;e of well and pile. ntructures where skin friction may be allowed on the pcrtion below the maxi:mum d~'pth of scour. ) t"e.sulting fro!n t1:-te (D) lllhere a substantial stratum of solid rock, or other material inerodible at the anticipated maximum velocity and of adequate safe bearing capacity, is encoJntered at a shallow depth below the surface, the foundatic•n shall be taken into that stratum and securely bonded or if necessary anchored to it. (E) Where only erodible strata are available, the fo:.mdations may be designed either as "Deep" or as ~:Shallow" but in such a manner that ii:l either case the safe bearing capacity of the sub~soil is not exceededo (1) DEEP FOUNDATIONS (in erodible strata) If 'd' is the anticipated maximum depth of scour below the designed highest flood level includ" ing that on account of possible concentration of flow, the minimum depth of foundation below H.F.L, shall be 1.33 d. The Depth below the scour line shall in no case be less than six feet for piers and 1-11
  17. 17. r------ ·---------- 1 HORIZONT.D..L CLElf.<ANCE ~·--------------~-----,--~--------~=------1 ' MINIMUM ROADWAY WIDTH :T LEAST 4FT. GREATER THAN APPROACH PAVEMENT WIDTH ..,1 BUT NOT LESS THAN 24 FT. CLEARANCE DIAGRAM TWO LANE HIGHWAY TRAFFIC FIGURE I Note: For heavy traffic roads, roadway widths greater than the above minima are recommended. For all bridges under 50 feet in length, the over-all width should conform as nearly as practicable to the full shoulder-to-shoulder width of the highway. For recommendations as to roadway widths for the various volumes of traffic see the Highway Design Manualo 1-12
  18. 18. abutments supporting other types of superstructure. The foundations shall in all cases be taken down to a depth vhich will provide proper grip according to some rational method. (2) SHALLmv FOUNDATIONS (in erodible strata). Foundations may be taken dmm to a comparatively shallow depth belov the bed surface provided the foundation bearing stratum is practically incompressible (e.g.sand), is prevented from lateral movement, and is also protected against scour. 1.9- SIZE OF CULVERT OPENINGS In general, culverts shall be proportioned to carry the maximum flood discharge without head. If the maximum flood discharge occurs only at rare intervals,culverts may be designed to carry i t under slight head, provided they are protected against undermining by means of adequate pavement and apron or cut-off walls and that adjacent embankments are protected from erosion by rip-rap or other suitable means. 1.10- LENGTH OF CULVERTS The length of culverts shall be sufficient to provide the required 1ATi.dth of roadway embankment. 111e assumed slope of the embankment shall be suitable for the particular filling material and shall be such as to eliminate any tendency for the embankment slopes to slip or slide. 1.11~ WIDTH OF ROAmvAY AND SIDEWALK The vidth of roadway shall be the clear width measured at right angles to the longitudinal centre line of the bridge between the bottoms of curbs or guard timbers, or, in the case of multiple height curbs, between the bottoms of the lower risers. The width of the sidewalk shall be the clear width, measured at right angles to the longitudinal centre line of the bridge, from the extreme inside portion of the handrail to top of the face of the curb or guard timber, except that if there is a truss, girder, or parapet wall adjacent to the roadway curb, the width shall be measured to its extreme walk side portion. 1.12· CLEARANCES The horizontal clearance shall be the clear width, and the vertical clearance the clear height, available for the passage of vehicular traffic as shown on the clearance diagrams. Unless otherwise provided, the several parts of the structure shall be constructed to secure the following limiting dimensions or clearances for traffic. The clearances and width of roadway for 2-lane traffic shall be not less than those shown in Figure 1. The roadway width shall be increased at least 10 feet and preferably 12 feet for each additional lane of traffic. 1-13
  19. 19. 1.13~ CURBS AND SAFETY CURBS The face of the roadway curb is defined as the battered or sloping surface on the roadway side of the curb. Preferably vertical c•.a-bs shall not: be used, Horizontal measurements of roadvn'l and curb >•Jidth q;::c_. given fTom cl:ce bottom of the face, or, in the case of stPp8ei back curb, fro~ the ~ottom of the lmver face for roadway width, The fuce of Lhe roadway curh pre fc-c-aLl;· sha 11 he not 1e::: s t!-.:n1 12 inche::; and in no instance less than 9 i.~•r:i--,".:·· !rc.m ::ha: p,wt :c:''' ,,f •:h·=: structu;,' above the elevation of the top of the CL.lTb awl n2are.st the road',vay. 1.r1 ca.;:;es of bridges in which the clear roadvJay widtr1 :i:; eqt:al !.o or great,,,, ,_:,,~;:-, th~; sho,~lder width but: not less than the approa~·rt pavenl9Et width plu:c; 12 fe.;>::, curbs may be omitted. In urban areas~ the cur~1 ht•igl1t shall no:. b"! less ~1-:;;..-::: 7 inches above the adjacent finished surfac(' of the :roadway, anr:l L1 -c;ra.l areas not less than 9 inches above the adjacent f ird. '-'h,:·.d "Jurfac2 of ttH~ rva(hvay. That portion of a curb more than 10 inches above the roadwa·y sur:-a.c~o: sba.ll b2 stepped back or sloped back so that no part of the vehicle except the tires may come in contact with it. Curbs widened to provide for occasional pedestrian traffic shall be designated "Saiety cnr::,3n. Safety curbs shall be not less than l 1 -6" wide. RAILINGS Railing shall be of traffic, or for the footpaths are provided between the two with a pedestrian railing may provided at the edge of scntctures for the prou-ci.:Lon protection of pedestria-::,s, or both. W11ere pe.d'::stri_':l!1 adjacent the roadways, n :r3.ffic railing ma.y he provided ~edestrian railing outsid2, or a combination trafficbe provided outside. Curbs shall be provided between roadways and a traffic barrier separates the two. A, pedP~trian footpaths unlesa TRAFFIC RAILING While the primary purpose of traffic railing i;> to contain the average vehicle using the structure, consideration should al2o be given to protection of the occupants of a vehicle in collision with the railing, to protecl:ioo of other vehicles near the collision, and to appearance a~d freedom of view of passing VBhicles. Material for traffic railing shall i::-e concre t.e, clletB.l, 1.mber c1· r-t combination. Metal materials with less than 10 per cent tested elongat:icn• shall not be used. Preference should be given to pro'Jiding a smootb, continuous face of rail on the traffic side with che posts set back £rom the face of the rail. Structural continuity in the rail members, including anchorage of free ends is essential. Where joints are required in the lengths of railings, the construction shall be reinforced by reduced post spacing, by splice material in the rails, by bolting or welding. 1-14
  20. 20. The height of traffic railing shall be not less than 2'-3" measured from the top of the roadway, or curb, to the top of the upper rail member. Careful attention should be given to the treatment of railing at the bridge ends. Exposed rail ends and sharp changes in the geometry of the roadway shall be avoided. B. PEDESTRIAN RAILING Railing components shall be proportioned commensurate with the type and volume of anticipated pedestrians, takir.g account of appearance, safety and freedom of view of passing vehicles. Materials for pedestrian railing may be concrete, metal, timber, or a combination" 1be minimum height of pedestrian railing shall be 3'-0" (a preferred height is 3'-6") measured from the top of the footpath to the top of the upper rail member, J., 15·- ROADWAY DRAINAGE The transverse drainage of road~vays shall be secured by means of a tmitable crown in the roadway surface and longitudinal drainage by camber or gradient. If necessary, longitudinal drainage shall be se~ured by means of scuppers, inlets or other suitable means, which shall be of sufficient ;.;J.ze and numbe:r to drain the gutters adequately. If drainage fixtures and downspouts are required, the downspouts shall be of rigid corrosion-resistant material not less than 4 inches in least dimension, provided with suitable clean~ out fixtures. The details of floor drains shall be such as to prevent the discharge of drainage water against any portior. of the structure. Over-hanging portions of con£rete floors preferably shall be provided with drip beads, L 16- SUPERELEVATION The superelevation of the floor surface of a bridge on a horizontal curve shall be provided in accordance with the geometric design criteria for highways, except that the superelevation shall not exceed .08 foot per foot width of roadway. L 17- FLOOR SURFACES All bridge floors shall have skid-resistant characteristics. 1. 18- UTILITIES Where required, provlslon shall be made for electric conduits, telephone conduits, water pipes and gas pipes. 1-15
  21. 21. 1. 1 :J- ROADWAY WIDTH, CURBS A~1D CLEARANCES FOR TUNNELS (See Figure 2.) (A) Roadway Tidth - The clear width bet,Jeen curbs shall be Lot than that specified for bridges. (B) Clearance bet'-Jeen Halls - The minimum ':vid th bet1een two-lane tunnels shall be 30 feet. (C) Curbs - The '#idth of curbs shall be not less than height of curbs shall be as specified for bridges. .U:J VJd lls lc~:-:o of ch.t~s. The (D) Vertical Clearanc:e - TI1e vertica1 clearance, betAJeen (::~1rbs sht1L1 be not less than 16'-6 11 • CLEARANCE DIAGRAM FOR TUNNEL TWO LANE HIGHWAY TRAFFIC FIGURE 2 1-16
  22. 22. F()tD!.1.Y t~)"j" CLEARANCE T~NO LA v~rlO-TH LESS YTi'-~i~.Pi .t'U11l FOR UNDER HIGHW.LW TRAFFiC FIGURE 3 1. 20- ROAmvAY WIDTH, CURBS AND CLEA.H;.NCES :FOR UNDERPASSES (UNDIVIDED HIGH-fAYS) (See Figure 3.) (A) -Jidths - The clear lividth betIeen -.;v-alls or columns shall be not less than 6 feet wider than the approach pavement, but in no case shall the width be less than 30 feet. (B) Vertical Clearance - A vertical clearance of not less than 16 '-6 11 shall be provided between curbs, or if curbs ar.e not used, over the entire width that is available for traffic. (C) Curbs - Curbs shall not be less than 18 inches in width, The height of curbs shall be as specified for bridges. 1-17
  23. 23. l. 21~ ROAmJAY WIDTH~ CURBS AND CLEARANCE FOR DEPRESSED ROADWAYS (A) Roadway Width-~ The clear vidth between curbs shall preferably be not less than that speciEied for bridges. (B) Clearance Between Walls - The minimum width between walls for depressed roadways carrying t>vo lanes of traffic shall be 30 feet. (C) Curbs= The width of curbs shall be not less than 18 inches. The height of curbs shall be as specified for bridges. 1-18
  24. 24. SECTION 2 - LOADS 2.1 - LOADS Structures shall be proportioned for the following loads and forces when they exist: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. Dead load Live load Impact or dynamic effect of the live load Wind loads Horizontal forces due to water currents Longitudinal forces caused by the tractive effort of vehicles or by braking of vehicles and/or those caused by restraint to movements of free bearings. Centrifugal forces Buoyancy Earth pressure Thermal forces Shrinkage stresses Rib shortening Secondary stresses Erection stresses Earthquake stresses. Hembers shall be proportioned as specified under stresses, Section 5 and 7. Upon the stress sheets a diagram or notation of the assumed live loads shall be shown separately. t-Jhere required by design conditions, concrete placing sequence shall be indicated on the plans. 2.2 - DEAD LOAD The dead load carried by a member shall consist of the portion of the weight of superstructure (and the fixed loads carried thereon), which is supported wholly or in part by the girder or member including its own weight. The following unit weight of materials shall be used in determining loads: Naterial Lbs./Cu. Ft. 1. Ashlar or Coarse Rubble Masonry 2. Brickwork 3. Cast Iron 4. Asphalt Concrete 5. Cement Concrete, plain 150 120 450 140 140 2-1
  25. 25. Materials Lbs./Cu.Ft. 6. Cement Concrete,reinforced 7. Earth (Compacted) 8. Macadam (binder premix) 9, Rolled Steel 10. Sand (loose) 11. Sand (wet compressed) 12. Stone Metal 13. Hater 14. Wood 15. Wrought iron A. 150 110 140 490 90 120 100 62.5 so 480 LOAD ON CULVERTS Earth pressure or load on culverts will be computed as the >veight of earth directly above the slab. B. RIGID CULVERTS For definite conditions of bedding and backfill, the principles of soil mechanics rnay be applied. The following are recommended formulas for these conditions: (1) Culvert in trench or unyielding subgrade, or culvert untrenched on yielding foundation. P = WH (2) Culvert untrenched on unyielding foundation (such as rock or piles) P W (1.92 H- 0.87B) for H P k 2, 59 BW ( e - 1) for H Where K = 0 · 385 > <:: 1. 7 1.7 B; B H B Where P the unit pressure in pounds per square foot due to earth backfill E width in feet of trench, or in case there is no trench, the over=all width of the culvert H depth in feet of fill over culvert w effective weight per cubic foot of fill material E 2.7182818 =base of natural logarithms,abstract number 2=2
  26. 26. C. SHEAR IN SLABS The maximum shear in the top and bottom slabs shall be assumed to occur at a distance out from the face of the wall or abutment eqL:al to the thickness of the slab, Hhen haunches are provided at the corners of the cells, their effect shall be excluded from the design. D. NEGATIVE MG1>1ENTS IN SLAB AND t;JALLS The maximum negative moments shall be taken at the face o£ the wall for the top and bottom slabs and at the underside of th6 top slab and top of the bottom slab for the walls or abutment, Bond shall be computed at the same section as for moments. 2.3- LIVE LOAD The live load shall consist of the weight of the applied moving load of vehicles, cars and pedestrians. 2,4- HIGHWAY LOADINGS General The highway live loading on the ro2v:hvays of bridges or incidental structures shall consist of a standa.rd truck ·· train. Two systems of loading are provided for Class nA" loading artd Class "B" loading, B. Class "A" Loading,. The class "N' loading ts illustrated in figure 4, a four-axle truck with two two-axle trailors .. C, It consists of Class "B 11 Loading The Class 11 B11 loading shall be identica 1 to Class ''N' loading except. for the axle loads which shall be 60';~ of Class A Loading. 2.5- STANDARD TRUCK - TP~IN LOADING The wheel spacing, weight distribution, and clearance of the standard loading shall be as shmv'l1 in Figures 4 with the following conditions; (1) Hthin curb to curb width of the roadway, the standard vehicle or train shall be assumed to travel parallel to the length of the bridge, and to occupy any position, which will produce maxhnum stresses, provided that the minimum clearanc-:es bstween a. vehicle and the roadway face of a curb and bet~veen two passing or crossing vehicles, as shown in figure 4, are not encroached upon,. (2) For each standard vehicle or train, all the axles of a unit 2-3
  27. 27. 10'-0" 65~~ 10'-0" 15,000 15,000 Lbs. __ Lbs. 15POO Lbs. 6,000 6,000 Lbs. Lbs. ~~ ·---N • .f"- ~---] :;------1 -----l --·---------:! s~~ .~ .. ""''"'1,_~-. CLASS OF LOADING r - s (, ' ;:,_ ~ i -1-~ . I'"E ........ ...J-..L.w.,.~-~"~~~"··· OF L!UITJNG POSITION STANOMD ''fRUCK ~TRAil! LOArHI•§G WITH REFERENCE TO A TRAFFIC LANE (For ground con! oct areo and value of ·~ •: se& tobh! i r.m<l 2 ) ll 15,000 _111"''-1 108 W zo 8 . ·-~---~6,00~-- ~- . ~ I "A'' GRrJl:JND CONTACTi WAD (L.hs) ----------r'2:5,ooo ·----------)";";1 --~ I ----- I. "B" ' ';:g~ L ___________ j__3, soo : 15 8 I ,'i _s __j______!__ _ TABLE I 'li0TE. Closs "e" loading will hove similar speGificotions to class "A" loading with the only differefce !hoi the oxie loads of class "a" :shall be oOfo of cia s s ':0.'~ --,-----------I'IJfl CLEAR ROAD WIDTH 16'- a" or less 0 16.- 8 .. to fa'-O"·pm;·.:;.:,eiog uniformly from o to 1':.. 4" 18'-0"to~ ditto 1'-tJ!'to 4'-o'' ~4'~__j__ _____ ._ 4'- o" ~ ------~ FIGURE 4 LOADING CLASS '~" FOR HIGHWAY BRIDGES TABLE 2 -r1
  28. 28. of vehicles shall be considered as acting simultaneously in a position causing maximum stresses. (3) Vehicles in adjacent lanes shall be taken as headed in the direction producing maximum stresses. (4) The spaces on the carriage vJay left uncovered by the standard train or vehicles shall be assumed as not subject to any additional live load. APPLICATION OF LOADINGS Truck-Train Units In computing stresses, each single standard truck-train shall be considered as a unit, and fractional widths or fractional trucks shall not be used, B. Numoer and Position, Truck-Train Loadings Th~ number of the truck train loadings and position as specified in Art. 2.5 shall be such as to produce maximum stress, subject to the reduction specified in Article 2.7. C. Continuous Spans On continuous spans one or both trailers sl-,:Jll be removed if vorst conditions are produced by doing so. 72 .' REDUCTION IN LOAD INTENSITY Where maximum stresses are produced in any member by more than one 3imultaneous truck=train load, the following percentages of the result;,;-~t ltve load stresses shall be used in view of improbable coincident maximum loading: Per cent One or two,truck-:· _;train ..Loadings '. : ·: ----·" ., - - - -"l Three ·nuck train load i_l1~.~-~ Four or more ·--~-~-- ~ 100 90 75 The reduction in intensity of floor beam loads shall be determined as in the case of main trusses or girders, using the number of truck train loadings which must be used to produce maximum stresses in the floor beam.
  29. 29. 2. 8- SIDEWALK, CURB, SAFETY CURB AND RAILING LOADING A. Sidewalk Loading Sidewalk floors, stringers, and their immediate supports, shall be designed for a live load of 85 pounds per square foot of sidewalk area. Girders, trusses, arches and other members shall be designed for the following sidewalk live loads per square foot of sidewalk area: Spans 0 to 25 ft. in length 85 lbs. Spans 26 to 100 ft. in length 60 lbs. Spans over 100 ft. in length according to the formula p P L W ( 55~1iJ --l so ! in >vhich live load per square foot (maximum, 60 lbs. per sq.ft) loaded length of a sidewalk in feet width of sidewalk in feet In calculating stresses in structures which support cantilevered sidewalks, the sidewalk shall be considered as fully loaded on only one side of the structure if this condition produces maximum stress. B. Curb Loading Curbs shall be designed to resist a lateral force of not less than 500 pounds per linear foot of curb, applied at the top of the curb, or at an elevation 10 inches above the floor if the curb is higher than 10 inches. Where sidewalk, curb and traffic rail form an integral system, the traffic railing loading shall apply and stresses in curbs computed accordingly. C. Safety Curb Loading Safety curbs, or wide curbs provided for occasional use of pedestrians, shall be designed for loads specified in paragraph (A) if the curb is more than 2 feet in width. If 2 feet or less in width, no live load shall be applied. D. Railing Loading (1) Roadway Railings Top members of roadway railings shall be designed to resist a lateral horizontal force of 150 pounds per linear foot together with a simultaneous vertical force of 100 pounds per linear foot applied at the top of the railing. When curbs are not less than 9 inches in height, lower rails shall be designed to resist a lateral horizontal force of 300 pounds per linear foot. 1iJhen curbs are less than 9 inches in height, this force shall be increased 40 pounds per linear foot for each inch the curb is less than 9 inches in height except that the adJed increment of horizontal force to be applied 2-6
  30. 30. to the lmver railing shall not exceed 200 pounds. If there is no lower rail, the web members shall be designed to resist a horizontal force of 300 pounds per linear foot applied not less than 21 inches above the roadway. For each inch of height of curb above 10 inches this lateral horizontal force may be reduced 15 pounds per linear foot, but this force Ehall not be less than 150 pounds per linear foot. The horizontal forces shall be applied simultaneously. Railingi:' without webs and with single rails shall be designed for the forces specified above for low2r rails. Sidewalk Railings (2) Sidevalk railings shall !:>e designed to resist the same forces as those specified for roadway railings, subject to the same restrict~ ions concerniHg curb heights. w11ere through trusses, girders, or arches separate the sidevwlk and road1vay or where side-walks are protected by curb railings, the sidewalk railings shall be designed only for the forces specified for the top rail. 2.9- IMPACT Live load stresses produced by the standard Truck-Train loading shall be increased for i terns in Group A by allowance as stated therein, for dyuamic ,, 'Jibratory and impact effects. Impact shall not be applied to items in Group B. (A) Group A (1) Superstructure) including steel or concrete supporting columns, steel towers, legs of rigid frames and generally those portions of the structure >vhich extend down to the main foundation. (2) The portion above the ground line of concrete or steel piles which are rigidly connected to the superstructure as in rigid frame or continuous designs. (B) Group B Abutments, retaining walls, piers, piles, except Group A(2) Foundation pressures and footings Timber structure Sidewalk loads Culverts and structures having cover of 3 feet or more (1) (2) (3) (4) (5) Impact Formula The amount of this allowance or increment is expressed as a fraction of live load stress, and shall be determined by the formula: (C) I = 15 L + 20 in which
  31. 31. I 1 impact fraction (maximum 30 per cent) length of span in feet For uniformity of application the span length "V' shall be especially considered as follows: For roadway floors, use the design span length. For transverse members, such as floor beams, use the span length of member centre to centre of supports, For computing truck load moments use the span length, except for cantilever arms use the length from moment ce.ntre to the farthermost axleo For continuous spans use the length of span under consideration for positive moment, and use the average of tvm adjacent loaded spans for negative moment. For bridges having cantilever acms with suspended spans, use the span of the cantilever arm plus half the length vf the suspended span when designing the cantilever and tti;:: span length of the suspended span designing the latter. For shear due to truck loads use the length of the loaded portion of span from the point under consideration to the far reaction. For culverts with cover O' H II i'f li 1' II II !! 1! 2' 2. 10,·· 1'' 111 to 1! to 2 I to 2' ~· ~ ~ O" inc, !=30~~ inc. llll inc. I=20'1o I=lO% on LONGI'I'UDINtL FORCES Provision shall be made for longitudinal forces arising from any one. or more of the follmving causes~· (a) Tractive effort caused through acceleration of the driving wheels or brak1ng effort from the application of the brakes to the braking wheels, This force shall be equal to ;'30/~ of the >veigt1.t. of the vehicle or any portion of the vehicle on the loaded span, the truck loads in one lane only being considered. For military loading this force shall be equal to ~-57;of the weight of the military vehicle, ·The centre of gravity of this longitudinal force shall be assumed to be located 6 feet above the profile grade of the roadway slab, , The change in the vertical reaction due to the transfer of the longitudinal force to the bearings 1 shall be accounted for. (b) Frictional resistance offered to the movement of expansion bearings due to change of temperature or any other cause. This force shall be equal to the dead load reaction multiplied by the coefficient of friction as shown below for the various 2-8
  32. 32. types of bearing: For roller bearings 0.03 For sliding bearings of hard copper alloy 0.15 For sliding bearings of steel on cast iron or steel on steel 0.25 For sliding bearingsof steel or ferro asbestos 0.20 For sliding bearings of concrete on elastomeric bearing pads 0.20 2 . 11- WIND LOAI1S The follm..ring wind load forces per squa-re fov t of exposed area sh::!ll hE:, B()plied to all structures (sec Article 5.1 for percentage of basic unit ,sc.re;,;s ~:o he used uuder various combiru-1tions of loads and forces). The '"xposed Hrl?d considered shall he the sum of the areas of all members, i:lclud-:Lng fJ.oox system and railing, as seen in elevation at 90 degrees to the .Longitudinal axis of the structure. The forces and loads given herein are for a wind VBlocity of 100 miles per hour. For Group II loading, but not br Group III loading, they may be reduced or increased in the ratio of the square 0f the design wind velocity to the square of 100, provided the maximum probable wind velocity can be ascertained with a reasonable accuracy,or ':here .are permanent features of the terrain which make such changes safe and advisable. If change in the design wind velocity is made, the design •vtnd velocity shall be shown on the plans. (A) Superstructure Design A moving uniformly distributed wind load of the following intensity shall be applied horizontally at right angles to thefiongitudinal axis of the structure :Ln the design of the superstructure:· For trusses and arches--,.c.-------------75 pounds per square foot For girders and beams --------------50 pounds per square foot The total force shall not be less than 300 pounds per linear foot in the plane of the loaded chord and 150 pounds per linear foot in the plane of the unloaded chord on truss spans and not less than 300 pounds per linear foot on girder spans. The above forces shall be used for Group II loading. For Group III loading there shall be added thereto a load of 100 pounds per linear foot at:plied at right angles to the longitudinal axis of the structure and 6 feet above the deck as a wind load on a moving live load. ~~en a reinforced concrete floor slab or a steel grid deck is keyed to or attached to its supporting members, it may be assumed that the deck resists within its plane, the shear resulting from the wind load on the moving live load. 2-9
  33. 33. (B) Substructure Design Forces transmitted to the substructure by the superstructnr-2 and forces applied directly to the substructure by wind loads shall be assumed to be as follows: Forces from Superstructure (1) The transverse and longittldinal forces transmitted by the superstructure to the substructure for varying angles of wind direct -ion shall be as set forth in the following table" The skew angle is measured from the perpendicular to the longitudinal axis, The assumed wind direction shall be that which produces the maximum stress in the substructure being designed, The transverse a:1d longitudinal forces shall be applied simultaneously at the elevation of the centre of gravity of the exposed area of the superstructure. Trusses Skew Angle of Wind (Degrees) Lateral Load per Sq, FL of Area (Pounds) Longitudinal Load per sq. Fto of Area (Pounds) 75 70 65 47 25 0 15 30 LJS 60 Girders 0 12 28 41 50 l,at:eral Load per Sqo Ft. of Area (Pounds) Long it ud ina 1 Load per sqo Ft. of Area (Pounds) 50 44 41 33 17 0 6 12 16 19 The loads listed above shall be used. in Group I I loading as given in Article 5" 1 For Group III loading, these loads may be reduced 70 per cent and there shall be added thereto, as a wind load on a moving live load, a load per linear foot as given in the following table: Skew Angle of Wind (Degrees) Lateral Load per Lin, Ft. ( Pounds ) Longitudinal Load per Lin. Ft. ( Pounds ) 0 100 0 15 30 45 88 66 12 24 32 60 34 38 82 This load shall be applied at a point 6 feet above the deck, For the usual gird2r and slab bridges having maximum span 2-10 "' "''
  34. 34. lengths of 125 feet, the following wind loading may be used in lieu of the more precise loading specified above. W ( wind load on structure) SO pounds per square foot, transverse; 12 pounds per square foot, longitudinal. Both forces shall be applied simultaneously. WL(wind load on live load) 100 pounds per linear foot, transverse; 40 pounds per linear foot, longitudinal. Both forces shall be applied simultaneously. 2) Forces applied directly to the substructure The transverse and longitudinal forces to be applied directly to the substructure for a 100 mile-per-hour wind shall be calculated from an assumed wind force of 40 pounds per square foot. For >vincl direction assumed skewed to t.he substructure this force shall be resolved into component[.; perpendicular to the end and front elevations of the substructure according to the functions cf the skew angle. The component perpendicular to the end elevation shall act on the exposed substructure area as seen in end elevation and the component perpendicular to the front elevation shall act on the exposed substructure area as seen in front elevation. These loads shall be assumed to act on horizontal lines at the centres of gravity of the exposed areas and shall be applied simultaneously vJith the wind loads from the superstructure. The above loads are for Group II ~oading and may be reduced 70 per cent for Group III Loading. (0) Overturning Forces The effect of forces tendi>:tg to overturn structures shall be calculated under Group II and Group III of Article 5.1. An up1vard force shall be applied at the 1.vind•-vard quarter point of the transverse superstructure width. This force shall be 20 pounds per square foot of deck and sideT.valk plaa area for Group II combination, and 6 pounds per square foot for Group III combination. The wind direct ion shall be assumed to be at right angles to the longitudinal axis of the structure. 2.12- THER~~L FORCES Provision shall be made for stresses or movements resulting from variations in temperature. The ri.se and fall in temperature shall be fixed for the locality in whL·h the structure is to be constructed and shall be figured from an assumed temferature at the time of erection. Due consideration shall be given to the lag between air temperature and the interior temperature of massive concrete members or structures. 2-11
  35. 35. The range of temperature shall generally be as follow Metal Structures Moderate climate from.0°to 120°F Extreme climate from minimum-30° F to 120° F Concrete Structure Moderate Climate Extreme climate 2.13- Temperature Rise 30° F '45°F Temperature Fall 30°F ·'"""'45'0 F UPLIFT Provision shall be made for adequate attachment of the superstructure to the substructure should any loading or combination of loading, increased by 100% of the live load plus impact, produce uplift at any support. 2.14- FORCE OF STREAM CURRENT (A) All piers and other portions of structures which are subject to the force of flowing water shall be designed to resist the maximum stress induced thereby. The effect of stream flow on piers shall be calculated by the formula: KV 2 p p = v = K = ' where Pressure in pounds per square foot velocity of water in feet per second a constant having the following values for different shapes of piers Square end piers Circular piers or piers with semi-circular ends Piers with triangular ends where the angle is 30 degrees or less Piers with triangular ends where the angle is more than 30 degrees but less than 60 degrees Piers with triangular ends where the angle is more than 60 degrees but less than 90 degrees Piers ends of equilateral arcs of circles Pier ends of arcs intersecting at 90 degrees 1. 50 0.66 0.50 0.50 - 0. 70 0. 70 - 0.90 0 .£~5 0.50 (B) The value of v2 in the equation P = KV 2 shall be assumed to vary linearly from zero at the point of deepest scour to the square of the maximum velocity at H.F.L. The maximum velocity shall be assumed to be equal to 1.4 times the maximum mean velocity of the current. (C) The intensity of pressure P, shall be applied to all portions of 2-12
  36. 36. the pier extending above the point of deepest scour. piles when a pile foundation is used. This will include (D) When the current strikes the pier at an angle, the velocity of the current shall be resolved into two components, one parallel, and the other normal to the pier. The value of the coefficient K to be applied to the component parallel to the pier shall be as per paragraph A of this article. The value of K to be applied to the component normal to the pier shall be 1.5 except for circular piers in which case the value will be 0.66. (E) When piers are designed parallel to flow an allowance of a 20 degree oblique flow shall be included in the design. 2.15sub~ BUOYANCY Huoyancy shall be considered as it effects the design of either the structure, including piling, or of the superstructure. 'No provision need be made for buoyancy if the bridge is founded on hcmogeneo'JS, impermeable strata. For bridges founded on coarse sand or shingle, ful1 buoyancy shall be allowed. For other foundation conditions, including foundations on rock, the calculated effect o£ buoyancy may be taken as a fraction of the full buoyancy, at the discretion of the engineer responsible for the design. 2.16- EARTH PRESSURE Structures which retain fills shall be proportioned to withstand pressure as given by Rankin 1 s formula; provided, however, that no structure shall be designed for less than an equivalent fluid pressure of 30 pounds per cubic foot. For rigid frames a maximum of one~half of the moment caused by earth pressure (lateral) may be used to reduce the positive moment in the beams, in the top slab, or in the top and bottom slab, as the case may be. "''hen highway traffic can come within a horizontal distance from the top of the structure equal to one half its height, the pressure shall have added to it a live load surcharge pressure equal to not less than 2 feet of earth. Where an adequately designed reinforced concrete approach slab supported at one end by the bridge is provided, no live load surcharge need be considered. All designs shall provide for the thorough drainage of the backfilling material by means of weep holes and crushed rock, pipe drains, gravel drains, or perforated drains. 2-13
  37. 37. 2.17- EARTHQUAKE STRESSES In regions where earthquakes may be anticipated, provlslon shall be made to accommodate lateral forces from earthquakes as follow: EQ = CD where EQ Lateral force applied horizontally in any direction at centre of gravity of the weight of the structure. D Dead load of structure C 0.02 for structures founded on spread footings on material rated as 4 tons or more per square foot. 0.04 for structures founded on spread footings on material rated as less than 4 tons per square foot. 0.06 for structures founded on piles. Live load may be neglected. 2.18- CENTRIFUGAL FORCES Structures on curves shall be designed for a horizontal radial force equal to the following percentage of the live load, without impact, in all traffic lanes: 6.68 s2 c == o.00117 s 2 D R where c s D R the the the = the centrifugal force in percent of the live load, without impact design speed, in miles per hour degree of curve radius of the curve, in feet The centrifugal force shall be applied 6 feet above the roadway surface, measured along the centre line of the roadway. The desigil speed shall be determined with regard to the amount of superelevation provided in the roadway. The traffic lanes shall be loaded in accordance with the provision of Article 2.5 and 2.6 When reinforced concrete floor slab or a steel grid deck is keyed to or attached to its supporting members, it may be assumed that the deck resists, within its plane, the shear resulting from the centrifugal forces acting on the live load. The effects of superelevation shall be taken into account.
  38. 38. Section 3 - DISTRIBUTION OF LOADS 3.1- DISTRIBUTION OF HHEEL LOADS TC STRINGERS, I.DNGITUDINAL BEAHS AND FLCC'"R 3EAHS (A) Position of Loads for Shea1 In calculating end shears a~d end reactions in transverse floor beams and longitudinal beams and str:i_ngers, no lateral or longitudinal distrihutioa of the ;,-Jheel load shall be assumed for the whee~ o-c axle load adjacent. to the end at which the stress is being determ~died. For lo.:ods in other positions on the span, the distribution for shear shall be determined by the method prescribed for moment. (B) Bending Noment in Stringers and Longitudinal Beams In calculating bending moments in longitudinal beams or stringers no longitudinal distribution of !:he wheel load shall be assumed. The lateral distribution shall be determined as follows: (1) Stringers and Beams The live load bending moment for each stringer shall be determined by applying to the stringer the fraction of a wheel load (both front and rear) determined by the following table: Kind of Floor Bridge Designed for one traffic lane Bridge designed for two or more traffic lanes Concrete: On steel I-beam Stringers (a) S/7.0 If s exceeds 1 ,, 1 v see note (b) On concrete Stringers (c) S/5.5 s exceeds 6' see note (b) If Concrete box girder (d) S/8.0 If s exceeds 12' see note (b) S/5.5. s exceeds 14' see note (b) If S/5.5 If s exceeds 14' see note (b) '' /:--; S/7.0 s exceeds 16' see note (b) If The dead load considered as supported by the outside roadway stringer or beam shall be that portion of the floor slab carried by the stringer or beam. Curbs, railing and wearing surface, if placed after the slab has cured, may be considered equally distributed to all roadway stringers or beams. 3-1
  39. 39. Notes: S (a) Design of I=Beam Eridge by N.M. Newmark-Proceedings, ASCE, March 1948. (b) In this case the load on each stringer shall be the reaction of the wheel loads, assuming the flooring between the stringers to act as a simple beam . (c) Design of Slab an~ Stringer Highway Bridges by N.M. Newmark and C. 2. C~ie:::;s~ Public Roads, January-:FebruaryMarch 1953. (d) (2) average stringer spacing in feet The sidewalk 1 iVt' load (see 2. 11) shall b2 omitted for interior and exterior box girders designed in accordance with the wheel load distribution indicated herein. . Total capacity of Stringers The combin~d design load capacity of all the beamb in a span shall not be le~:s than required to support the total live a~. d dead load in the span, (A) Span Lengths ( See also Article 6.2 ) for simple spans the span lengU! shE-ill bP the distar"cce cec,tre c:o cc:ntre of supports but not to exceed clear span plus thickness of slab. The following effective span lengths shall be used in calculating distribution of loads and bending moments for slab continuous O'.'er more th&n two supports: Slabs monolithic with beams or walls (without haunches) S Clear Span Slabs supported on steel stringers S (B) distance between edges of flanges plus stringer flange width ~ of the Edge Distance of Wheel Load In designing slabs the centre line of wheel load shall be assumed to be 1 foot from the face of the curb. 3-2
  40. 40. (C) Bending Moment Bending moment per foot ~·7id~h methods given under Cases A and H. o[ sJab shall be calculated according to In cases A and B: S Effective span length, in feec, as defined under "Span Lengths" (Art. 3.2(A) and 6.2) E Width of slab in feet over vhich the load is distributd P Load on one wheel of truck 12,500 pounds for Class A loading 7,500 pounds for Class B loading Case - A Hain Reinforcement perpendicular to traffic The live load moment per foot width of slab for a simple span shall be determined by the following formula (Impact not included) M (S+2) P/25 In slabs continuous over three or more supports a continuity factor of 0.8 shall be applied to the above formulas for both positive and negative moment. Case - B Main Reinforcement Parallel to traffic For distribution of wheel loads E 2+0.68 For roadway widths K = 7.0 1 X K >- 28' :;;;- 1 For roadway widths ~ 28' Roadway width K 14 x Number of Truck Train Load -ings Truck train moments for continuous spans and simple spans, except as noted, shall be determined by suitable analysis and distributed over a width of 2E. The lateral distribution of wheel loads for multi-beam precast concrete bridges shall not exceed that specified for slabs. The live load-moment per foot width of slab for simple spans shall be determined by the following formulas. 3-3
  41. 41. (Impact not included) For simple spans up to 35' Use N == 0.9S K X For simple spans 35' to 70' Use H = (1.35 (D) c ..:> - 16) X 1Z (Foot )~ips) Edge Beams ( Longitudinal) Edge beams shall be provided for all slabs having main reinforcement parallel to traffic. The beam may consist of a slab se.ction adrlitionally reinforced, a beam integral with and deeper than the slab, or an integral reinforced section of slab and curb. It shall be designed to resist a live load moment of 0.5 x simple span truck train Moment Value for continuous spans may be reduced 20 per cent unless a greater reduction results from a more exact analysis. (E) Distribution Reinforcement Reinforcement shall be placed in the bottoms of all slabs transverse to the main steel reinforcement, to provide for the lateral distribution of the concentrated live loads, except that this specification will not apply on culverts or bridge slabs when the depth of fill over the slab exceeds two feeL The amount shall be the percentage ·:;Jf the main reinforcement steel required for positive moment as given by the follovJing formula: For rnain rein.forcemer.;_t parallel to ':raffic; 100 .F'or :nr:~i:1 Where S ~FOr icular to traffic: ::20 rei·nforce:rnent p = the 0ffective spa~ l~2grh, Lfi teet rna. i.n rein for c ent£;·nt per pe-c1f.i i c u la t· Lo t r s. f f i ~ th ~~ s pe-e· if Led ctJnou n ~.:: o.t distribution reinforc.ern,=::nt sl:all bt~ us2d i the rntddle half of the spc.n but t~Il_i.~ may be reduced by 50% in the end quarLers of the span. Longitudinal reini:orcement. in tLe top of slab ha,Jing ti:H' main reinforcement perp,:>nd icu1ar ro traffic shall not be les:~ rhail 0, 20 square inch per foot of widt:h.
  42. 42. (F) Shear and Bond stress in Slabs Slabs desi~ned for benrlin~ moment in accordance with the foregoing shall be considered satisfactory in bond and shear. (G) Unsupported Edges, Transve:·se The design assumptions of . . his article do e10t pro'Jide for the effect of load near unsupported ·c::dges. There fore, at the ends of the bridge and at intermediate points ';~here the continuit.y of the slab is broken, the edges shall be suprcrted by diaphragms or other suitable means. The diaphragms shall be designed to r2sist the full moment and shear produced by the wheel loads which can come on them. (H) Cantilever Slabs Under the following formulas for distribution of loads on cantilever slabs, the slab is designed to support the load independent of edge support along the end of the cantilever. Case A. Reinforcement Perpendicular to Traffic Each wheel on the element perpendicular to traffic shall be distributed according to the following formula: E o.6x+2.5 PX Moment per foot of slab = - E in which X = distance in feet from load to point of support Case B. Reinforcement Parallel to Traffic The distribution for each wheel load on the element parallel to traffic shall be as follows: E 1.2X + 1.6 For roadway widths ~ 28' E max 7.0 X K K= 1 For roadway widths <28' Roadway width K= 14x Number Truck Train Load in In calculating the moments one axle load of 36000 lbs. may be substituted for the two 25000 lbs tandem axles of the standard truck train if this produces a greater stress. 3-5
  43. 43. (I) Slab Supported on Four Sides In the case of slabs supported alo~:tg four edge;o. and reinforced in both directions the proportion of the load carried by the short span of the slab shall be assumed as gi'Jen by the follmving equations: b4 For load uniformly distributed, p a4 + b4 b3 For load concentrated at centre,p a3 + b3 ifhere p proportion of load carried by short span a = length of short span of slab b length of long span of slab Where the length of the slab exceeds 1~ times its width, the entire load shall be assumed to be carried by the transverse reinforcement. The distribution vidth, E, for the load taken hy either span Bhall be determined as provided for other slabs. Moments obtained shall be used in designing the centre half of the short and long slabs. The reinforcement steel in the outer quarter of both short: and long spans may be reduced 50 per cent. In the design of the supporting beams, cons ideratio•1 shall be given to the facr that the loads rle}h!ered to thE· supporting beaws are not uniformly distributed along the beams. 3. 3- DISTRIBUTION 01: lrT!:lt<:E1~ l.OPI.DS T!:lR01!GFi EAR'f!-1 .FILLS Whe!t the depth of fill is 2 fe;~t or more, conceEtrated loads shal i he considered as uniformly distributed over a square, the sides of >:vhich an: equal to 1-3/4 times the depth of fill. 'i.l!e shear produced by such loads shall be calculated as provided for dead loads. When such areaa from several concentrations overlap, the total load shall be considered as uniformly distributed over the area defined by t:he outside limits of the individual areas, but J:h.e tota1 vJidth of distrihnion shall nor exceed the total width of the supporting slab. For single span the effect of live load may be neglected when the dept.h of fill is more tlH:trl 8 feet and excec.;ds the span length; for nmltipl2 spans it may be neglected ,,Jhen the depth of fill exceeds the distance betveen races of enJ supports or abutments. When the depth of fill is less than 2 feet the 1-iheel load shall be distributed as in slabs with concentrated loads. V.Jhen the calculated live load and impact moment in co::1crete slabs based on distribution of the wheel load through fills· as herein outlined exceeds the live load and impact momen! calculated according to Article 3.2 then the latter moment shall be used. 3-6
  44. 44. Section 4- l-'l.ILITARY LOADING 4.1- LOADING 1':'1e military loading on the roadways of bridges or incidental structures shall consist of 70 long ton tracked vehicle as shown in Figure 5 subject to the restriction that the nose to tail distance between two successive vehicles is not less than 300 feet. No other live load shall cover any part of the roadway of the bridge when this vehicle is crossing the bridge. Only one such train shall occupy the roadway of the bridge. ..... "'v ~ "v co ,.._ 00 ,.._ (/) (/) -0 z z ~ I -C1 0 1- 1n J'() 10 J'() 70 TON MILITARY LOADING FIGURE 5 4-1
  45. 45. HORIZONTAL CLEARANCE The minimum clearance betweec-1 th2 rc.advn:;.y i;:;.ce o"" ctcrb and the outer edge of ch2. track shall be assumf'd aH tollo"'rs ~ ..Jid th ot roadway 11 1 -6 1; to 13' ~6<1--====•c•===== 1'-0" 13 '-6! 1 to 18 '-0''=====-==~~~ 2'=0 11 4'·~0n 4,3= Unless a more exact annlysis is made the 70 T be distributed to the stringers as indicat;;:d ':ielow~ 4.4- ~1ilitary L:J&d shall IMPACT Live load stresses shall be increased for items in Group AJ n,,ferred to in Article 2.9 by an allowance as stated herein, for dynamic vibratory and impact effects. Impact shall not be applied to items in group B referred to in article 2.9. A, Impact Formul§J:. 1. Concrete Structures Spans less than 30 feet Spans 30-150 feet Spans greater than 150 feet., , 2. 25% 10/~ 8. 8/o Steel Structures Spans less than 30 feet All spans greater than 30 ft •• 4.5- DISTRIBUTION OF LOADS AND DESIGN OF CONCRETE SLABS (A) Span lengths (B) 25% 10/o Edge distance of track See Art. 3.2 In designing slabs the center line of track shall be assumed to be minimum 1'-6" from the face of curh, 4-2
  46. 46. (C) Bending Moment B..::r::ding moment per foot of -;,d.d::J·; or s:c;.b sha.lJ. be according to methods give.n nnder Ca.se':; A and B, calcDlat2c~ In cases A and B: s E~fective "~)pan span length ~n feet, as defined under Length (Article 3,2.)n E Width of slab in f6et over which a track is P Load on one track Case A - = di~tributed 78.4 Kips (35 Long tons) Hain Reinforcement Perper1dicular to 'iraffic Moment for simple spans L 1 s For spans continuous ·over three or more supports use 0,.8 x simple span moment for both positive and negative moment. Case B :Main Reinforcement Parallel to Traffic For simple spans greater than 12 feet M P(S-~6) /I..~E For simple spans less than 12 feet For moments in continuous spans a suitable analysis shall be used. The width of distribution, E, shall be computed as follows: .458 + 4.0 4-3
  47. 47. Section 5 -· UNIT STRESSES 5.1 GENERAL Unless otherwise noted the allowable unit stresses indicated herein are given in pounds per square inch. The following groups represent various combinations of loads and forces to which a structure may be subjected. Each part of such structure or the foundation on which it rests, shall be proportioned for all combinatio~s of such of these forces as are applicable to the particular site or type, and at the percentage of the basic unit stress indicated for the various groups except that no increase in allowable unit stresses §.lJ..aJLb.e perglitted for members or conn~-~tions carrying wind loads oniy. See article 2.1 to 2.l8 fOr 'Toads. and forces. The maximum section required shall be used. Percentage of Unit Stress ..;,{"'' ". :..~l<"'#8~>1'11~ Group Group Group Group Group Group Group Group Group '.D IL l /I 'E I II III IV v VI VII VIII IX ;B w WL LF CF F R S T EQ SF ICE D+L+I+E+B+SF D+E+B+SF+W ,... ' .....-~ .·/. ;; "·~- ~--··-,;· . Group I+b.~+F-1-CF+~p% ~;2-!!,&i' == Group I+R+S+T .. - ......· Group II+R+S+T = Group III+R+S+T - D+E+B+SFilEQ} == Group I+fcE == Group II+ICE Dead Load = Live Load Live Load Impact / (, = Earth Pressure Buoyancy == Wind Load on Structure Wind Load on Live Load-100 pounds per linear foot = Longitudinal Force from Live Load = Centrifugal Force Longitudinal Force due to friction Rib Shortening Shrinkage == Temperature Earthquake Stream Flow Pressure Ice pressure . 5-1 100% ··125% 125% 125% 140% .140% 133% 140/o 150% r I
  48. 48. 5.2- CONCRETE STRESSEs(i) (A) Standard Notations and Assumptions fc = Permissible Extreme fiber stress in compression Unit ultimate compressive strength of concrete. as determined by 6 inch cube tests ar: 28 days, f 1c (f'c) == n Unit ultimate compressivE: strength of concrete as determined by 6" cylinder test at 28 d::tys. ratio of modulus of elasr.icity of steel to that of concrete. The 'value of n, as a function of the ultimate strength of cone:. rete, shall be assumed as follows: Cube f 1c :::: 2600 3200 3800 5100 6000 Cylinder 3100 3700 5000 5.'·900 or more (f'c) = 2000 2500 3000 = 4000 = 5000 - 2400 2900 3900 4900 or more n=l5 n=l2 n=lO n= 8 n= 6 for computations of deflections the value of n=8 shall be used. Coefficients: Thermal Shrinkage. (B) .000006 ,0002 per Allowable Stresoes (ii) (1) :flexurco. Extreme fiber in compression. Extreme fiber in tension 0 plain concrete, primarily in footings-------------------= Extr·.::me fiber in tension,. reinforced concrete--------- Cube Strength fc= 0.33 f'c Cylinder Strength 0.40(f'c) ft:= 0,025 f'c O.OJ(:Cc) None None The ratios and --:,ralues in thiB SE,ction apply to concrete made with convef1t -ional hard rock aggregate, values applicable to light weight aggregate concrete should be established by adequate investigation, (ii) In no case shall the allowable stresse.s be basE:d on an ultimate cube strength greater than 5800 psi or ultimate cylinder strength greater than 4500 psi except for prestressed concrete. 5-2
  49. 49. (2) Shear Cube Strength Beams without web reinforcement Longitudinal bars not anchored or plain concrete footings---- 0.016 f'c 0.02(f'c) Max 75 psi Longitudinal bars anchored 0.024 f'c 0.03(f'c) Max 90 psi Beams with web reinforcement V=0.060 f'c bjd 0.075(f'c)bjd Horizontal shear in shear keys between slab and stem of T beams and box girders (3) Cylinder Strength 0.12 f'c O.lS(f'c) 0.08 0.10(£' c) BonJ, Deformed bars: With deformation complying with specifications ASTM A 305 Straight or hooked er:ds,exclus= ive of top bars (a) In beams, slabs, o~e way footiu.gs, (b) In two w.TJ footingt: B(;'Y, of mw ;,1ay footi.Tt>U' Top bars= Hsrs t1F:ar top o~: b?BElS and gird·:;rs having more thBn 12 inches of concrete under th8 bar2 0.05 f 1 c For plain bars the ed by 5W, 5 ' ,,,= ) VBll1fcS 0.06 list:nd ior defonued bB.rs sh,;ill be d.ecn,as- REINFORCJ<:MFNT Nild Steel co;:tforming to -!LS, 785 or A3'i'H A15 ~)peci:ficHtionR SteP.l P.e:Lnforcement: Tens ion in flexural nerr!bersc" ------ ··-- --18,000 Te::~s ioD in web men1aers~ --- -·-- ~ -~·--~- --18, 000 Compress ior1 in co lum::::.s~ -- ---=---- -----13 ~ 200 Co;!ipression in 5.4= SIEE~ Steel Parr: 3 B, be;;tr:lS See Article 6. 6 STRESSES stre~>SE-s shall conforn, to the British ;Jesign Sta:1{'iard 153 Stresses, of the British Standard Institution 1958 Edition. 5-3
  50. 50. SECTION 6 - CONCRETE DESIGN 6.1- GENERAL ASSUMPTIONS The design of reinforced concrete members under these specifications shall be based on the following assumptions: (1) Calculations are made with reference to unit working stresses and safe loads, as elsewhere specified herein, rather than 1iJith reference to ultimate strength and ultimate loads. (2) A plane section before bending remains plane after bending. (3) The modulus of elasticity of concrete in compression is constant within the limits of working stresses; the distribution of compressive stress in flexure is, therefore, rectilinear. (4) The ratio 11 n" shall be assumed as follows: Value of n Es Ec Ultimate strength of concrete, Lbs. per sg.in. 6 11 cube 6 11 cylinder ]trength strength 2600 3200 3800 5100 6000 - 3100 3700 - 5000 - 5900 or more 2000 2500 3000 4000 5000 - 2400 2900 - 3900 - 4900 or more For computations of strength 15 12 10 8 6 For computtation of deflection 8 In computing the ultimate deflection of slabs and beams, the value of the modulus of elasticity should be assumed as one-thirtieth that of steel in order to allow for the effect of plastic flow and shrinkage. (5) Concrete shall be assumed as offering no tensile resist- ance. (6) The bond between concrete and metal reinforcement is a.s;:;umed to remain unbroken throughout the range. of working stresses. Under compression the two materials are therefore stressed in proporation to their moduli of elasticity. (7) Initial stress in the reinforcement due to contraction or expansion of the concrete, is neglected, except in the design of reinforced concrete columns. 6-1
  51. 51. (8) For the determination of external reactions, moments, shears, and deflections, moments of inertia of rigid frame and continuous structures shall be computed for the gross concrete sections, neglecting the effect of steel reinforcement, except that the transformed area of the steel 3hall be included for columns, arches or other compressive members. 1be moment of inertia of the entire superstructure sections, except railings or any curbs or sidewalks not placed monolithically with the superstructure before the falsework is released, and the moment of inertia of the full cross section of the pier or bent shall be used to determine the elastic properties of the various spans-and supports. (9) (10) The depth of girder or L~lab to be used in computing momer1t of inertia at the centerline of the support shall be ohtair1ed by extending the slope of the intrados of the member to the centerline. (11) Rigid frames ahall be considered free to sway longitudinally due to the application of vertical dead loads and vertically applied live loads except when the structure is restrained from movement by extertEll forces. (12) The assumption of no moment restraint at the base of column shall be m<'3d in the analysis of rigid fra:nes (superstructures) unlsss the bas~=: is knmvn to be fully fixed. When a pim!ed end condition is assumed for the analysis of the superstructure, the base of column, footing and piling shall be designed to resist the mor.1ent resulting from a!l a2sumed restraint varying from zero to full fixity. The degree of restraint shall he deterrt1i.ned by the type of footing and the character of the foundation material. (13) Piers or bents constructed integrally with footings placed on a skew exceeding 10° shall be considered fixed at the top of footing. 6.2- SPAN LENGTHS The effective span lengths of slabs shall be as specified in Article 3. 2. The effective span length of freely supported beams shall not exceed the clear span plus the depth of beam. For the analysis of all rigid frames, the span lengths shall be taken as the distance between the centres of bearings at the top of th12 footings. The span length of continuous or restrained floor slabs and beams shall be the clear distance between faces of support. 6.3- EXPANSION In general, prov~s~on for temperature changes shall be made in all simple spans having a clear length in excess of 40 feet. 6-2
  52. 52. In continuous bridges, prov~s~ons shall be made in the design to resist thermal stresses induced or means shall be provided for movement caused by temperature changes. Expansion not otherwise provided for shall be provided by means of hinged columns, rockers, sliding plates or other devices. 6.4- T-BEAMS (A) Effective Flange Width In beam and slab construction, effective and adequate bond and shear resistance shall be provided at the junction of the beam and slab. The slab may then be considered an integral part of the beam, but its assumed effective width as a T-beam flange shall not exceed the following: (1) (2) (:3) One fourth of the span length of the beam. 1he distance centre to centre of beams Twelve time the least thickness of the slab plus the width of the girder stem. For beams having a flange on one side only, the effective overhanging flange width shall not excet.~d one twelfth of the span length of the beam, nor six times the thickness of the slab, nor one half the clear distance to the next beam. (B) Shear The flange shall not be considered as effective in computing the shear and diagonal tension resistance ofT-beams, except in the determination of the value of j. The horizontal shearing unit stress at the juncture of the. flange and the monolithic fillet joining it to the girder stem shall not exceed that given in Article 5.2(B)(2), shear of beams with web reinforcement. (C) Isolated Beams Isolated beams, in which the T-form is used only for the purpose of providing additional compres:::io::1 area, shall have flange thickness of vot less than one-half the width of the web, and a total flange width of not more than 4 times the width of web. (D) Diaphragms For T-beam spansJdiaphragms or spreaders shall be placed between the beams at the middle or at the third points. 6-3
  53. 53. (E) Construction Joints When a construction joint is required between the slab and the seem of the beam, the shear-keys shall be designed in accordance with allowable stresses given in Article 5.2(B)(2). 6.5- REINFORCEMENT (A) Spacing The minimum spacing centre to centre of parallel bars shall be 2~ times the diameter of the bar, but in no case shall the clear distance between the bars be less than 1~ times the maximum size of the coarse aggregate. (B) Covering The minimum covering, measured from the surface of the concrete to the face of any reinforcement bar, shall not be less than 2 inches except in slabs where the minimum covering shall be 1 inch at the bottom and P2" at the top. Where an additional wearing surface is to be used the required clearance at the top of slab may he reduced to 1". In the footings of abutments and retaining walls and in piers the minimum covering sh<:tll be 3 inches. In work exposed to the action of sea water the minirlmm covering shall be 4 inches except in precast concrete piles 3 where a minimum of 3 inches may be used. For stirrups in T-beams, the minimum cover shall be. 1~ inches. (C) Splicing Tensile reinforcement shall not be spliced at points of maximum stress. When reinforcement is spliced, the spliced bars shall lap sufficiently to develop the full strength in bond. (D) End Anchorages and Hooks End anchorage may be an extension of the bar, either straight, bent or hooked. A properly dimensioned hook is: (a) one in wb.ich the bar is bent: in a complete semi-circular turn with a radius of bend on the axis of the bar of not less than three bar diameters, plus an extension at the free end of at least four bar diameters?(b) a 90° bend having a radius of not less than four diameters plus an extension of twelve bar diameters. Hooks having a radius of bend of more than six bar diameters shall be considered as extensions to the bars. Hooks shall not be considered effective in adding to the compressive resistance of bars. Any mechanical device capable of developing the strength of the bar without damage to the concrete may be used in lieu of hooks or extensions. (E) Extension of Reinforcement (1) To provide for contingencies arising from unanticipated distribution of loads, yielding of supports, shifting of points of inflection, or other lack of agreement with assumed conditions governing the design of elastic structure, the reinforcement shall 6-4
  54. 54. be extended at the supports and at other points between the supports as indicated in (2) to (5) below. These paragraphs relate to ordinary anchorage and are the minimum requirements under which normal working stresses for bond or shear are permitted. (2) Negative tensile reinforcement at the supported end of a restrained or cantilever beam or member of a rigid frame shall be extended in or through the supporting member in such a manner as to develop the maximum tension in the bar with a bond stress not exceeding the normal working stress provided in Article 5.2. (3) Between the supports of continuous or simple beams, every reinforcement bar shall be extended at least 25 diameters but not less than 1/20 of the span length, beyond the point at which computations indicate i t is no longer needed to resist stress .A i!-typ•:o hcok si:1al1 be: co:.~sidered equal tc' 16~ and an I, type hook equal to (4) In simple beams and freely supported ends of continuous beams, at least 1/3 of the positive reinforcement shall extend beyond the face of the supports a distance sufficient to develop ~ the allowable stress in the bars. s-,. (5) In restraiued or continuous beams at least i; of the positive reinforcement shall extend beyond the face of the supports and the remainder treated as provided in (3). (6) Dowels and bars carrying little or no theoretical stress should be embedded at least ten bar diameters from the construction joint. (F) Maximum Sizes lbe maximum size of bar reinforcement shall be 1~ inches in diameter, unless the particular conditions warrant the adoption of special reinforcement design. When structural steel shapes are used for reinforcement, mechanical bond should be provided which will effectively bond the memher to the surrounding concrete mass. (G) Position of Negative Moment Reinforcement in I-Beams Wben the floor slabs or flange of a continuous or cantilevered T-beam is placed after the concrete in the stem has taken its set, at least 10 per cent of the negative moment reinforcing steel shall be placed in the beam stem in order to prevent cracks from falsework settlemert or deflection. 'This reinforcing steel shall extend a distance of one-fourth the span length each side of t:he intermediate supports of continuous spans, one-fifth the span length from the restrained ends of continuous spans, and tte entire length of cantilever spans .In lieu of the above requiremer:.t two number 6-5
  55. 55. 8 bars full length of the girders may be used ( ") n Reinforcement of Beam Sides The depth of the beam between the main reinforcement and the flange or the top reinforcement shall be reinforced with horizontal bars in both faces to prevent temperature and shrinkage cracks. The total area of steel in each face shall not be less than eq. in. per foot of height of the unreinforced beam side. The spacing of bars shall not exceed 2 feat. 6.6- COMPRESSION REINFORCEMENT II~ BEAMS Compression reinforcement in girders and b~ams shall be secured against buckling by ties or stirrups adequately anchored in the concrete, and spaced not more than 16 bar diameters aparL Where compression reinforcem~nt: is used, its effective;:-~.ess in resisting bending ma:Y' be tc:~ken as twice th~ ·.;alue indicated from the calculations as3uming a straigh t-1 ine relation between stress and strain and the modular relatio~ of stress in steel to stress in concrete given in Article 6.1(4). However, in no case should a str~ss in compression reinforcement gr2ater than 16,000 pounds per square inch be allowed. 6.7= WEB REINFORCEMENT (A) Gt:c.neral When the allowable unit shearing 3tres& for concrete is exceeded, web reinforcement shall be provided by one of th<::: following methods: (1) (2) (3) Longitudinal bars bent up in s0ries or in single plane. Vertical stirrups. Combination of bent-up bars a:<1d vertical stirrups. Wh.er1 any of the above methods m: reinforcement are used, tb.e concrete may be assumed to carry external vertical shear not to exceed .024 f' (cube strength) or . 03 (f~), (cylinder strength) (Maximum 90 pounds per sq~are inch) the remainder of shear being carried by the web reinforcement. The we~s of T-beams and box girders shall he reinforced with stirrups in a 11 cases, (B) Calculation of Shear and Bond Diagonal tension, shear, and bond iQ reinforced concrete beams shall be calculated by the following formulas: NOTATIONS: A v total area of web reinforcement in tension within a distance 6-6 11 s 11
  56. 56. (measured in a direction parallel to that of the main reinforcement), or the total of all bars bent up in any one plane. b width of beam. d effective deptl-1, or depth from compression surface of beam to centroid of tension reinforcement. tensile unit stress in web reinforcement. j ratio of lever arm of resisting couple to depth ;;d". s spacing of web reinforcement bars, measured at the neutral axis in a direction parallel to that of the main reinforcement. u bonJ stress per unit area of the surface of the bdr. v shearing unit stress V' external shear on any section after deducting shear carried by concrete. sum of perimeters of bars angle between web bars and axis of beam FORMULAS: Shearing unit stress, as a measure of diagonal tension v v bjd Stress in vertical web reinforcement f v V' s When a series of web bars of bent-up longitudinal bars are used, the reinforcement shall be designed by the following formula: V' s fv jd ( sinO:+ coso() When the web reinforcement consists of bars bent up in a single plane so as to reinforce all sections of the beam which require reinforcement, the bent-up bars shall be designed by the following formula: 6-7
  57. 57. V' A f v sino( 1be bond between concrete and reinforcing bars in beams and slabs shall be computed by the following formula: u v jd ~0 (For approximate results 11 j 11 in the above formulas may be taken as 7/8) Bond shall be similarly computed on compressive reinforcement, but the shear used in computing the bond shall be reduced in the ratio of the compressive force assumed in the bars to the total compressive force at the section. Anchorage shall be provided by embedment past the Bection to develop the assumed compressive force. (C) Bent-up Bars Bent-up bars used as web reinforcement may be bent at any angle between 20 and 45 degrees with the longitudinal reinforcement. The radius of bend shall not be less than 4 diameters of the bar. The spacing of bent-up bars shall be measured at the neutral axis and in the direction of the longitudinal axis of the beam. l'his spacing shall not exceed thre.:~~fourths the effective depth of the beam. The first bar from the support shall eros~ the mid-depth of the heam at a distance from thE face of the support, measured parallel to the longitudinal axis of the beam, not greater than one=half the effective depth. (D) Vertical stirrups Where stirrups are required to carry shear, the maximum spacing of vertical stirrups shall be limited to !;z the depth of the beam, and where not required to carry shear, the maximum spacing shall be limited to 3/4 the depth of the beam. The first stirrup shall be placed at the distance from the face of the support not greater than one- fourth of the effective depth of the beam. (E) Anchorage (1) The stress in a stirrup or other web reinforcement shall not exceed the capacity of its anchorage in the upper or lower one-half of the effective depth of the beam. (2) Web reinforcement which is provided by bending into an inclined position one or more bars of the main tensile reinforcement where not required for resistance to positive or negative bending, may be considered completely anchored by continuity with the main tensile reinforcement, or by 6-8
  58. 58. embedment of the requisite length in the upper or lower half of the beam provided at least one half of such embedment is as close to the upper or lower surface of the beam as the requirements of fire and rust protection allow. A hook placed close to the upper or lmver surface of the beam may be substituted for a portion of such embedment. (3) Stirrups shall be anchored at both ends by one of the following methods or by combination thereof: ' (a) Rigid attachment, as by welding, to the main longitudinal reinforcement. (b) Bending round and clostly in contact with a bar of the longitudinal reinforcement, in the form of a U-stirrup or hook. (c) A hook placed as close to the upper or lower surface of the beam as the requirements of fire and rust protection will allow. In estimating the capacity of this anchorage the stress developed by bond between midheight of the beam and the centre of bending of the hook may be added to the capacity of the hook. (d) An adequate length of embedment in the upper or lower onehalf of the effective depth of the beam, whether straight or bent. Anchorage of this type alone should not be relied on for stirrups in cases where the shearing stress in the web exceeds that recommended for beams without end anchorage of the reinforcement. (See Article 5.2) 6.8- COLUMNS (A) General Other provisions of Section 6, Concrete Design, shall apply in the design of columns unless specially modified by this article. In the design of columns the unsupported length shall be defined as the clear distance between struts, cross beams, footings or other types of adequatE restraint to lateral movement. Where a bracing member has haunches at its junction to a column, the unsupported column length shall be measured from the junction of the haunch with the column provided that the face of the haunch makes an angle with the face of the column of at least 45 degrees.StrutE or cross beams joining columns at angles greater than 30 degrees from the plane of symmetry of the column shall not be considered as adequate support. 6-9
  59. 59. The least lateral dimension of a column shall be taken as: (1) for rectangular columns, the over-all thickness along a principal axis; (2) for spirally reinforced columns, the overall diameter including the encasement of the spirals; (3) for HT 11 -shaped columns, the width or depth of the T. In a column which, for archic:ectural or other reasons, has a larger cross section than required by the load carried, the minimum amount of longitudin::tl steel hereinafter specified may be reduced provided that in no case shall less 'longitudinal steel be used than that: required by the mir:imum column designed with one per cent of longitudinal steel. The notations used in this article are as follows: over~all or gross cross-sectional area of spirally reinforced or tied pier, pedestal or column in square inches. cross-sectional area of core of spirally reinforced columns measured to the outside diameter of the spiral, square inches. As = A cross-sectional area of longitudinal steel Ag + (n-1) As , effective area of column fa c fa or factor used in the design of members subject to combined axial and bending stresses least lateral dimension of column, inches 0.30 f'c* d e eccentricity of resultant load on a column, measured from a gravity axis. f'c = crushing strength of 611 cubes at age of 28 days, psi (f'c)= crushing strength of 6"xl2" cylinders at age of 28 days, psi . .J. 0.175 f~" + fs p for spiral columns and fa 1 + (n-1) p 80% of that amount for 0.225(f'c) + fs p tied columns. or 1 fe fs * 'ld~ + (n-1) p maximum allowable compressive stress in members subjected to combined axial and bending stress, psi. nominal working stress in longitudinal reinforcing steel (see Article 5.3) 6-10 6" cube strength 6 11 cylinder strength

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