structural principle

1. 1
GENERAL PRINCIPJtJE§
'flHDE lFlUNC'fliON OJF A lBillJL][))ING
A shelter is basically a protection from the external environmental elements and the function
ofa building is to enclose space so that a satisfactory internal environment may be created
relative to the purpose ofthe particular building. That is to say, the space within the building
must provide conditions appropriate to the activities to take place within it and satisfactory
for the comfort and safety ofany occupants. Thus the space will be designed in terms of §izte
and sllnap~ and in terms ofernrvfirrollllml!Helllltt.llll fadorr~ such as wea{ffan and llTJOif§e exc!U~Jsimm, and
the prmvisim11 of111deqouJJte !ttem, light lllirMl air. The fabric ofthe building must be designed to
ensure that any standards in respect to these are attained.
A building consists ofthe following elements to satisfy the purpose ofdesign.
Srill'Mctoar111l System
The structural system ofa building is designed and constructed to support and transmit
applied gravity and lateral loads safely to the ground without exceeding the allowable
stresses in its members. Structural system ofa building consist ofthe following elements;
., The superstructure is the vertical extension ofa building above the ground.
" Columns, beams, and loadbearing walls support floor and roof structures,
o The substructure is the underlying structure below the ground level forming the foundation
ofa building.
Enclos011re System
The enclosure system is the shell or envelope ofa building, consisting of the roof, exterior
walls, windows, and doors.
o The roofand exterior walls shelter interior spaces from inclement weather and control
moisture, heat, and airflow.
o Exterior walls and roofs also dampen noise and provide security and privacy for the
occupants ofa building.
" Doors provide physical access.
" Windows provide access to light, air, and views.
$Interior walls and partitions subdivide the interior ofa building into spatial units.
· Mec!umal and ElectricalSystems
The mechanical and electrical systems ofa building provide essential services to a building.
" The water supply system provides potable water for human consumption and sanitation.
" The sewage disposal system removes fluid waste and organic matters from a building.
$Heating, ventilating, and air-conditioning systems condition the interior spaces of a
building for the environmental comfort ofthe occupants.
e The electrical system controls, meters, and protects the electric power supply to a building,
and distributes it in a safe manner for power, lighting, security, and communication systems,
o Vertical transportation systems carry people and goods from one level to another in
medium- and high-rise buildings.
o Fire-fighting systems detect and extinguish fires.
o High-rise structures may also require waste disposal and recycling systems.
I
I
I

2. S{v-.c.iv.rlfiu'
S. ~ ~ ---e V-
Roof Systems
Moisture &Thermal
Protection
Floor Systems
Special Construction
,.,,
Doors & Windows
Mechanical &
Electrical Systems
• ' . ' ! '
Wall Systems
Finish Work
Foundation Systems

3. Wigwam
The building fabric must be of such a nature that it can withstand safely all the forces to
which the building will be subjected in use. In other words it must have a ~tlll!M:tu!.ire~
This structure is a result ofa fabrication. and does not move in any appreciable manner under
its loads. Buildings vary widely in form and appearance but throughout history they have all
developed from three basic concepts of structure. These are known as :§Jkddatll9 ®®llndl and
:§llllrlace :§tl:Jrlllldllilir~§.
SlkeDeU:aH §tl:rnndruure
As the term implies this consists essentially ofa skeleton or framework which supports all
the loads and resists all the forces acting on the building and through the skeletal system all
loads are transferred to the soil on which the building rests.
Simple examples are the North American Indian shelters and the mid-European wigwam;,s
in which a framework ofpoles or branches supports a skin or tree bark or leafs enclosing
membrane.
This elementary form ofa building has developed throughout history into frameworks
which consist essentially ofpairs ofuprights supporting spamling member as shown in the
following figure as f:S8aeilframe, rigid/fromre and !Jll!l.iUdli!iBifffno.lJ'iliJe structures. These are
spaced apart and tied together by longitudinal members to form the volume ofthe building.
In these frames the vertical supports are in compression .
Shed frame Rigid frame
co lumns ----ll--1
FRAMED OR SKE L ETAL CONSTRUCT ION
Building
frame

4. §keleta! structures in which the floom are suspended fmm the li:op ofthe building by vertt:icZJJ
elements in tension are generally called 3lli.J3jperal!k!!li <l!lll" §M$J!Pt!T!a$B@!!a stmcrures.
Other forms ofthe skeletal structure are known asgli'id §tv'l!IJ.~d(I!J.iN!3, an example ofwhich is
shown in the figures below.
By its nature the skeleton frame cannot enclose the space within it as an environmental
envelope and other enclosing, elements must be associated with it. The significance ofthis
clear distinction between the supporting element and the enclosing element is that the latter
can be made relatively light and thin and is not fixed in its position relative to the skeleton
frame- it may be placed outside or inside the frame or may fit into the panels ofthe :frame
as may be seen in examples ofcontemporary steel or concrete frame structures. Skeletal
structures are suitable for high and low rise, and for long and short span buildings.
§onn~ llllt!itllldnmr~
In this form ofstructure the wall acts as both the enclosing and supporting element. It falls,
therefore, within the category oflaHodlJelfJJri/J1J,g wOlll structures, an inclusive term implying a
structure in which all loads are transferred to the soil through the walls. The characteristic of
>(/spenslon structure GrJd structure Transfer of loads
this particular form is a wall ofsubstantial thickness due to the nature ofthe walling
materials and the manner in which they are used, such as in masonry and mass concrete
work.
The Eskimo igloo is an interesting example ofthis type ofconstruction (figure 1.2) although
for technical and economic reasons circular plan forms have been less used than rectangular
forms for buildings constructed in this way.
Solid construction in the form ofbrick and stone wall buildings has been used over the
centuries and, in certain circumstances, in its various modern forms it is still a valid and
economic type ofconstruction for both high- and low-rise buildings. See the following
figure..
SOLID CONSTRUCTION
load beo;ing
walls
d 1. d usually to buildings oi
structurally limite con 1ne ·
tow height and short spans

5. Zulu hut
Cellular structure Transfer
Cross wall siructure
§unri~~Ee ~ttwundunwe
Surface structures fall into two bro21.d groups
(i) those in which the elements are made ofthin plates ofsolid material which are
given necessary stiffness by being curved or bent, and
(ii) those in which the elements consist ofvery thin flexible sheet membranes
suspended or stretched in tension over supporting members.
A Zulu woven branch and mud hut ( shown in the following figure) and modern reinforced
concrete &!kelll andfoUded &lab structures are typical ofthe first. In this form also the wall,
and the roof, may act as both the enclosing and supporting structure but the manner in which
particular materials are used results in quite thin wall and roofelements.
of loads
Shell vault
Folded or bent slab
Shell dome
Those in the second group are used for roofs and are known as ltemuln®llll §twundllllll'~§. One
form is typified by the traditional Bedouin tent (See the following figure) ofwhtch
delightful modern applications are available.
Utilising suitably developed membranes this form can now be used for roofing permanent
structures. There are several examples ofthis type ofstructures in Bahrain.
suspension roof
Air supported
structure
Bedouin tent
2 Structural concepts

6. Another form in this group, using ~t<lliiiDD!Jllrrte§§~«!l ~ii!r as the supporting medium for simi!ar
types ofmembrane. . In thls the membrane is fixed and sealed at ground level and is
tensioned into shape and supported by air pumped into the interior and maintained under
slight pressure (see the following figure).
Alternatively, inflated tubes may be incorporated which form supporting ribs to the
membrane stretched between them. These are called fflJEii'=§!lDJ!bU.Ui&eai orJlPil!leMIYU11$Jrlic §g!l'&actl&al!'ef§J.
In a third form in this group the &M&J!Pieftft§OilPllit &tv'ou:t&are& where the membrane consists of steel
cables suspended from supports and carrying a thin applied cladding and weatherproof
covermg ..

7. Introduction Structure is an important and integral part of nature and architecture. The
survival ofanimal and plant life found in nature depends upon their ability to develop a
8l1l:wundUlllanll SJyS11l:~m, through their growth patterns, which fulfills their functional
requirements. Structure in architecture must also be developed as an integral part of its total
design.
Animal and plant life constantly resist external pressures and forces exerted upon them and
resolve these forces within their structural systems to survive.
Living forms are able to prevent structural failure in many instances by moving with the
force, while in architecture applied loads and forces must be resolved within an immovable
structure.
The ability ofboth nature and architecture to successfully resolve forces within their
systems is dependent to a large degree upon the mma~~1l:rell"n2ill ofthe structural elements and the
get!llmell:ry oii'11:lllle §y§ttremm.
The choice of an appropriate structural system in architecture is based on a knowledge ofthe
physical properties of materials and an understanding offorc~s and stresses. The validity of
this decision will be revealed in the total design.
:Fowc<es
A force can be defined as that which tends to exert motion, compression or tension on a
body .A designer is concemed with the resolution offorces so that a structure will remain in
equilibrium .
Figure 1 illustrates many ofthe forces which must be resisted by a building and resolved
within its structural system. These forces are can be classified as two types <Gravnty ll([J)ad§
and L::nltell"ai ll@ad§.
Growity load& are caused by the gravitational pull ofthe earth and act in the vertical
direction. Therefore, they are also referred to as vertical loads. Gravity loads include the
materials and components that comprise the buildings, as well as people, rainwater, snow,
furniture, equipment, and all that is contained within the building. Gravity loads are further
classified as dead lmad& and live lolf!Jds,.
•
• •
•
1.1 LIVE LOADS AND DEAD LOADS
load of roof cov~rings plus
any ~now and win.d load!:>
tronsfl!:rr~d t o r oof m!l:mbrz:rs
loads; acc~pted by
roof members trans.ferred
to walls~
tot~ floor loads t
·tr.onshrred to
wo"
l l t ,
ceiling joi$lS
dead and live loads
of flooring transferred
to floor:- joi sts ·
total f tOor loods. .
trons! errttd to
int«:rnol load
beorin'g wo!l · .
wall loads
·tronsferrt d
_
to. foundations
ground floor loads+ f
tror.s..fcrr~d dire:c l
to ground
t otal wall toads. tron~ie:rrtZ:d I +
v.io foundot~ons to. o s.uito~lq-_j
'loOd bearing copoctty s.ub ., o!l
6

8. The two primary sources ofU@l.JJerr!JJU 0@«1Mi!3 on buildings are ~-vfmn«l! and ~&ll.Irtllnqjllll&lllk~§. The .
effect of each is to create loads in the lateral (other than vertically downward) direction. For
example, wind creates horizontal forces on a wall as well as vertically upward forces
(suction) on a:flat roof
The main effect ofearthquake ground motion is to create horizontal forces in buildings,
although a small amount of vertical force may also exist. Additional examples oflateral
loads are ertllrih JPF!f!§§B!We @IYd lbtfll§ement Wtflllff§, wmerrpre&§!J!Jll'e @n d@r;nJk wCJ.UU§, and loads caused
by !h!CJ.§/1B OJ!!iJd J10Wwing we!Jaff!:Ue§ or equipment. . .
Another way ofclassifying the loads acting on a buildings is as ,static, dynamtc and 1mpac;
St@tic load§
.Static loads are assumed to be applied slowly to a structure until it reaches its peak value
withoutfluctuating rapidly in magnitude orposition. Under a static load , a structure
responds slowly and its deformation reaches a peak when the static force is maximum.
Dynamic Uot!llil3
Dynamic loads are those which change rapidly. The rapid changing nature ofthese loads
can cause some unusual behavior in buildings, which can result in structural failure. Under a
dynamic load , a structure develop inertial forces in relation to its mass. The two major type
ofdynamic loads are wind loads and earthquake loads.
Impact lolld&
Impact loads are those which are applied suddenly. The dynamic effects of an impact load
are at least twice as large as the static effects ofthe same load applied slowly.
Ifa 1-lb weight is placed slowly on a spring scale, the scale hand will stop at the 1-lb mark.
Ifthe weight is held just touching the scale and released suddenly, the hand will jump to 2
lb. oscillate, and eventually stop at the 1-lb mark.
Ifthe weigh: is held about 3 inches (in) above the scale and dropped, the hand will reach the
4...1b mark before coming to rest at the 1-lb mark. The higher the drop height, the greater the
impact velocity, and the greater the impact load .
The sudden sideways movement ofthe ground under a building caused by an earthquake is
an impact load ofparticular importance in building structures. The effect is the same as that
created when a truck traveling at a constant speed is suddenly stopped by applying the
brakes. The wheels ofthe truck stop immediately, but the inertia (momentum) ofthe higher
and more massive truck body tends to
These live and dead loads induce forces and stresses within the structure which are
classified as either compression, tension, shear, torque, or bending.
Comp:r~§Si®n
A compressive force tends to condense material. Figure 1.2 illustrates a block which has
been deformed by the application ofopposing external forces. These external forces pushing
against the block cause the material to become more compact or dense.
Figure 1.3 shows an example ofcompressive forces in nature. The weight ofthe stones at
the top ofthe pile causes compression in the lower stones. The lower stones support the
weight ofall the stones above and resist a greater compressive force than the top stones.
This same principle can be observed in architecture (Fig. 1.4). This column is composed of
stones which have been cut and laid to support a compressive force resulting from applied
loads.

9. -
c-----------
-----..'
'
- -- ---- -- - - -- - - -~
1.2 COMPRESSION
1.3 COMPRESSION IN NATURE
1.4
COMPRESSION IN ARCHITECTURE
TeHRsnmm
A tensile force tends to stretch material. Figure 1.5 illustrates a bar which has been
deform~~ ~~ the application ofopposing external forces. .
These forces stretch the bar and cause tension within the material.
An example ofa tensile force in nature is illustrated in Fig 1 6 The weight ofthe spider
exerts a pull upon its supporting thread causing this thre~d to be in tension A suspension
bridgee (Fig 1 7) illustrates tensile forces at work in a man-made structure The main
curvilinear suspension cables and the vertical cables supporting the road bed are in tension.
1.7 TENSION IN A STRUCTURE
8

10. 1.5 TENSION
1.6 TENSION IN NATURE
~ Compressive force ~
(a) Acable (or rope) presents no
resistance to an applied compressive
force. Hence t he st ress in cable = zero.
Suspension cable
(in t ension) - --<Y
/1
FIGURE 4.5 Tensile and compressive stresses in the members of a suo
sion bridge.
+m- Tensile f orce ~
(b) A cable (or rope) would resist an
a pplied t ensile force. Hence, therewould
be a finit e tensile st ress in the cable~.
FIGURE 4.3 Stresses in a cable under (a) an applied compressive force and (b) an applied tensile force.
§lln®a!ll"
A shearing force tends to divide an object along a plane parallel with the opposing external
forces. Figure 1.8 illustrates a shearing action. The block shown in this figure has been
separated by the two opposing parallel forces.
Shearing action may be observed in nature. The cantilevered ledge shown in Fig. 1.9 must
resist tremendous shear forces. Shearing forces, in addition to tensile and compressive
forces, exist in practically all the members ofa structural system. .
1.8 SHEAlR
1.9 SHEAR IN NATURE

11. 'fq])lf((}l_1l}l€:
shearing force, p
p shearing stress N = p 1 A
Figure 2. 14: Shearing stress N = shearing force P divided by area being
sheared A.
. twi§t an object resulting in a shearing stress.
Torque is the result offorces whteh tend to ther an'd cause the block to deform.
. . · p· 1 10 oppose one ano
The two twtstmg forces m 1g. · . . t'lon ofour body produces torque.
. . · ture Every twtstmg mo . 1 ·
Torque ts qmte common m na . . d "ll lt ;.,. ~structural failure. Ftgure 1.1 ts an
. h . t d ately restste Wl resu ll-1. "'
Torque whic lS no laf:e'qlu caused by insufficient resistance to torque.
example ofstructura at ure .
1.10 TORQUE
l.ll TORQUE IN A BEAM
Bending is the result offorces which tend to deflect a member by inducing tension,
compression, and shear. The block in Fig. 1.12 is being deformed by forces which cause
bending.
(}
Forces which cause bending are a common occurrence in nature, and the structures ofnature
must resist these bending forces The stem ofthe flower shown in Fig 1 13 can be bent by
the wind. Internal tensile and compressive forces must resist bending or the stem will break.
Bending in a beam is caused by external forces as shown in Fag 1 14 The external load or
force will cause this simply supported beam to develop internal resistive forces of
compression in the top and tension in the bottom The beam will not fail ifthe material is
sufficiently strong to resist these internal forces.
1.12 BENDING
l.l4 BENDING IN A BEAM
0

12. n.
1.13 BENDING IN NATURE
(a) Beam before bending (b) Beam after bending
fiGURE 4.15 Demonstration of bending in a beam. In a beam bent with a water-holdi ng curvature, as shown in (b), the upper half of the
beam is in compression and the lower half of the beam is in tension.
10
{1
0
Internal forces cause stresses within structural members A stress can be defined as a force
per unit area, and is indicated by the formula: f (stress) = P (force) +- A (area).
An internal force in a structural member which causes a stress in a material greater than the
resistive capacity ofthe material will result in structural failure. Therefore, sufficient area
must exist within a structural member to resist these internal forces.
Stress can be illustrated in the following examples. Figure 1.15 shows a 1 inch by 1 inch
block resisting an external load of 10 pounds. The tensile stress in this block can be found
by dividing the load (10 pounds) by the area (1 square inch) which is equal to 10 pounds per
1.15 A ONE SQUARE
INCH BLOCK
U.7 SHEAR IN A FOUR SQUA._Fill
INCH BLOCK
1.16 A FOUR SQUARE
INCH BLOCK

13. square inch. Another example (Fig. 1.16) shows a block with a cross sectional area of4
square inches resisting a load of 50 pounds The. compressive stress in this block can be
found by dividing the force by the area and is equal to 12 1/2 pounds per square inch. A
shearing stress equal to 5 pounds per square inch is illustrated in Fig. 1.17. This shearing
stress is found by dividing the force (20 pounds) by the cross sectional area (4 square
inches).
The stress produced in a portion ofa building's structure is illustrated in Fig. 1.18. In. this
example the column has a cross sectional area of 144 square inches and supports a load of
36,000 pounds. The stress in the column is determined by dividing the load by the cross
sectional area and is equal to 250 pounds per square inch. To determine the stress per square
foot, divide 36,000 pounds by the cross sectional area of 1 square foot. This stress is 36,000
pounds per square foot.
The load supported by this column must be transferred to the ground. A stress of36,000
pounds per square foot would probably be too great for the soil to support. To avoid
overstressing the soil, the base ofthe column (footing) has been enlarged to spread the load
over a greater area (f= PIA). This footing is 3 feet by 3 feet or equal to 9 square feet. The
load transferred.from the footing to the soil would be: 36,000 pounds divided by 9 square
feet or 4,000 pounds for each squarefoot.
1.18 COLUMN AND FOOTING
1.19 CONCENTRATED LOAD ON SNOW
1.20 SNOW SHOE ON SNOW
•
1.21 CONCENTRATED LOAD IN HEEL
Additional examples of stress may be observed in the following two illustrations. Figure
1.19 illustrates what might happen ifa man tried to walk on snow without snow shoes. The
large stress in the snow is created by the man's weight distributed over the small area ofhis
foot. Ifthe man weighs 200 pounds and the cross sectional area ofhis shoe is 30 s~uare .
inches, the stress in the snow under his foot is approximately 7 pounds per square mch. The
size ofhis foot is not sufficient to spread his weight over enough area to prevent the snow
from compressing under the load. When a snow shoe is used, as illustrated in Fig. 1.20, the
load will be distributed over a larger area, and the stress within the snow will be
considerably less. Ifthe area ofthe "Snow shoe is 10 times larger than the area ofthe man's
shoe, the stress on the snow is 1110 of7 pounds or less than 1 pound per square inch.

14. Ligm toaus (.;Uncenuau;;u wnmn a vt:ry smau area wm proauce 1arge srr~:sst::s . !'Igure l.L.l
shows that the stress in a woman's heel may be quite large if her weight (120 pounds) is
concentrated within the small area ofthe heel Ifthe heel is V4 inch by 114 inch, the area wiU
be 1/16 ofa square inch The stress within the heel is 120 pounds divided by 1/16 ofa square·
inch or 1,920 pounds per square inch. This stress is sufficiently large to crush many
materials.
A moment may be defined as a force acting on an element through a distance. This is
illustrated in Fig. 1.22. The force (P) times a lever arm (L) can be expressed by the formula:
M=PxL.
A moment is illustrated in Fig. 1.23. Ifa man extends his arm 1 foot and holds a brick
weighing 5 pounds, the moment created about the man's shoulder is relatively small: 5
pounds times 1 foot or 5 foot pounds. Ifhe extends his arm 3 feet, then the moment is
greater and the load seems heavier. This moment is 5 pounds times 3 feet or 15 foot pounds,
plus some additional moment created by the weight ofthe arm.
Moments in a beam are found in the same manner. Figure 1.24 shows a 20 foot beam with a
load of :n.090~0 pounds concentrated at the center. To find the moment at the center ofthe
beam, multiply the end reaction (5,000 pounds) by the lever arm (10 feet). The moment is
50,000 foot pounds. The beam must resist this moment internally just as the shoulder ofthe
man had to resist the moment caused by the brick.
L
1.22 MOMENT = FORCE x DISTANCE
p
0 1.23 MOMENT IN A MAN'S ARM
1.24 MOMENT IN A BEAM
JEffed @if §jp)~ll!B ~nndl dep~llu @if be~m ®Hll §tJrenngtllll
Figure 1.25 shows how the internal resisting forces within a beam can be illustrated. The
internal forces are larger at the center and gradually decrease toward the supports. The
internal resistive moment within the beam is also reduced as the external moment is
reduced~ however, the internal moment must be equal to the external moment ifthe beam is
to resist the applied load.
The distance between the internal compressive and tensile forces is an important factor in
the design ofa beam. Figure 1.26 shows the internal forces as they might appear in two
different beams one shallow and one deep In the shallow beam the forces are large because
the distance (lever arm) between these forces is small, while in the deep beam the forces are
considerably smaller because the lever arm is larger This would generally mean that less
material is required to resist internal forces in deep beams.

15. 1.25 FORCES IN A JBEAM
1.26 FORCES IN A SHALLOW
BEAM AND A DEEP BEAM
The importance of depth in beam design is illustrated in Fig. 1.27. When a flat piece of
paper is held at one end only, it will easily bend under its own weight because the internal
lever arm is extremely small Ifthe paper is folded, as illustrated in Fig. 1.28, the lever arm
ofthe resisting moment is large, and the paper will not bend under its own weight.
This same principle can be observed in nature. A smallflat leaf supported at one end
deforms easily (Fig. 1.29). A corrugated palm leaf supported at one end could extend much
further without deformation (Fig. 1.30). Its increased depth provides the necessary
re~istance to prevent bending.
1.27 BENDING IN A
SHEET OF PAPER
~-:~:·
1.28 FOLDED PAPER
1.29 BENDING IN A LEAF
1.30 FLUTED PALM LEAF

16. The efficiency_ofa beam is increased by making the section deep with most ofthe material · 5 ·
at the extremities-farther from the neutral axis-where the maximum bending stresses
occur.
Beam depth is an important consideration for reducing bending stresses and limiting
vertical deflection.
Deeper beam~ are subjec~ to later~l buckling due to the stress caused by the external loading.
Lateral buc~hn? can b~ mduc~d. m. a structural member by compressive stresses acting on a
slender portion msuffictently ngui m the lateral direction.
Increasing the beani width increases the beams resistance to lateral buckling.
c~n-nnmJID§
The geometrical shape ofa structural member plays an important role in its ability to resist
bending forces and support loads. It is difficult to stand flat sheets ofpaper on edge. In this
condition the paper is unstable and will buckle and collapse under its own weight as shown
in Fig. 1.31. When the paper is rolled into a circular tube, as illustrated in Fig. 1.32, it can
support more than its own weight.
This same principle may also be observed in nature. A flat blade ofgrass bends under its
own weight, as shown in Fig 1. 33. Some grasses, however, are able to grow several feet
without bending because oftheir circular cross section This is illustrated in Fig 1. 34
These examples indicate that column sections can sustain heavier loads ifthey are round,
square, or have a large proportion oftheir material at the periphery (Fig. 1.35).
Less efficient column shapes are essentially flat and, therefore, easily bent under heavy
loads.
The length ofa column influences its load carrying capacity. This can be illustrated with a
yardstick. When a man leans on a yardstick, shown in Fig. 1.36, it will easily bend under his
weight, but a short section ofthe same yardstick will be difficult to bend.
-
1.31 lPAPER COLUMN 1.32 VERTICAL PAPER 1.33 FLAT GRASS BLADE

17. 1.34 CIRCULAR GRASS
STEM
0
I D
1.35 EFFICIENT COLUMN SECTIONS
Efif~d of M211tteri~ll§ OID S1hrtellll.gttlhl
1.36 YARDSTI:CK
Applied loads cause internal resistive forces in structural members which in tum produce
stresses within these structural. members. Ifthe types ofstresses can be determined, then an
appropriate material can be chosen to provide a stable and efficient structural system.
Some ofthe more common building materials used in structural systems are shown in Table
1.1. This table shows that the ability ofa material to resist forces varies considerably.
Steel, for example, is extremely strong in tension while concrete and masonry are very
weak in tension. Wood is strong in tension although it has less than one tenth the tensile
strength ofsteel.
Steel is almost as efficient in compression as it is in tension. However, the shape and
unsupported length ofa steel member affects its ability to resist compressive forces
effectively without bending. . .
. . 1h hits design capacity in compresslOn ls o~ly.one.
Concrete is strong m compresslOn abt ~ug t al vt·rtue is compression is often hmlted m
1 M whose as1c struc ur ' ffi · ·
tenth that of stee . asonry, W d like steel is nearly as e 1c1ent m
load bearing capacity by the strength ofthe mortar. oo , ,
compression as it is in tension.
Table 1.1
Range of design stresses for typical structures in pounds/square inch
I
TENSION COMPRESSION SHEAR
:00,000 10,000 14,0()(1
Stl'<'l to to to
200.1100 22,000 20,000
50 1,000 50
Cont'rl'tt~ to to to
100 2,250 80
1,000 1,000 100
Yo~ 1d to to to
2,400 2,000 150
50 200 0 to
las! lllr>· to to 100
100 400
Tla·~t' strt>sses ''./ill ,·ary dt>pending upon a numbt>r of variables su(;h as
Jll;.lll..:ritll L'tllllJ)I)Sition, c:ros:-;: St>dion and length.
·I

18. §ttJrle§§~§ linn lBS®<ffifJIIll§
§tresses within a beam will vary from zero at the center ofa symmetrical beam to a
maximum stress at the top and bottom edges. Sincethe stresses near the center are relatively
small, the area in the central section ofthe beam does not utilize the stress potential ofthe
material. Figure 1.37 shows a rectangular section and illustrates approximate distribution of
bending stresses within the section.
Rolled sections of steel are designed to place material at the top and bottom where it is most
effective. Figure 1.38 shows a wide flange steel section and illustrates the stress distribution
within this section. The stress diagram indicates that additional material near the center
would not appreciably increase the efficiency ofthe section. The small additional resistance
to bending, made possible by additional material near the center, would not sufficiently
increase the efficiency ofthe beam.
---
1.37 RECTANGULAR BEAM AND
STRESS DIAGRAM
1.38 WIDE FLANGE BEAM AND
STRESS DIAGRAM
Concrete, as previously mentioned, is very weak in tension but strong in compression. When
only concrete is used in a beam, the lower portion ofthe concrete will easily pull apart and
beam will fail. However, when steel rods are placed in the lower portion of a concrete
beam, they effectively resist tensile forces in this area. This beam takes structural advantage
ofthe concrete in compression and the steel in tension. Figure 1.39 shows a section through
a portion ofa concrete slab and illustrates how the stresses are distributed within this slab.
Note that the concrete is highly stressed at the top ofthe slab and that this stress drops
to zero near the center. The steel takes all ofthe tensile stress in the lower portion ofthe
slab.
The concrete in the lower half ofthe slab is used only to hold the steel in place. Ifsome of
the concrete between the steel bars is removed and the steel bars grouped, a concrete joist
system is formed, as illustrated in Fig. 1.40.
··;,.:.
~"
1.39 CONCRETE SLAB AND
STRESS DIAGRAM
H
J
1.40 CONCRETE JOIST AND
STRESS DIAGRAM

19. The efficiency ofthe system increases as the depth ofthe joist is increased.
Removal ofthe excess concrete in the lower portion, which was not ofstrvJctural value,
reduces the dead load andprovides greater live load carrying capacityfor the system. The
material required for a concrete joist system will be considerably less than that required for
a slab system ofequal span and load.
Compressive
Neutral plane,
generally referred
to as neutral axis
stress r--.~..,--.~¥/
Tensile
stress
Compressive
stress
stress (a) Beam in three dimensions
· Stress distribution on a small length, PQSR, of the beam in Figure 4.15 .
FIGURE 4.16 The location of the neutral axis in a beam under
bending stresses. Note that the neutral axis is, in fact, a neutral
plane. It is called the neutral axis becau se we generally draw a
beam in two dimensions-in cross section-in w hich the neutra
plane is shown as a line.
tunreinforc.ed c.onaete beam
fails in tension(c.racks on bottom)
st eel reinforcing in bottom
of beam resists tension
Figure 8.5: Bending in a concrete beam without and with steel re.lntorcing.

20. Reinforced concrete beams depending on the stresses develop can be reinforced in two
different ways.
A ::siumgUy=l?eovifm"l[;<eifi !!Je@Tltle is one in which the concrete eiem.:en~ is only relinforced near the
tensile face and the reinforcement, called tension steel, is designed to resist the tension.
A ®aafbUy=reiV'Dfm·cedl /be(D,m is one in which besides the tensile reinforcement the concrete
element is also reinforced near the compressive face to help the concrete resist compression
The latter reinforcement is called compression steel When the compression zone ofa
concrete is inadequate to resist the compressive Moment(positive moment), extra
reinforcement has to be provided ifthe architect limits the dimensions ofthe section.
Pz:·e=&llii'e§&oV'Dg
Neither the concrete joist system nor the concrete slab system takes fhll advantage of
concrete's ability to resist compressive forces over its entire area. Concrete is utilized more
efficiently in systems which primarily resist compressive forces.
One method ofobtaining a better utilization ofconcrete in beams is by pre-stressing orpost-
tensioning the concrete. Figure 1.41 illustrates a simple concrete beam under load. The dark
triangle represents tensile stress and the lined triangle represents compressive stress in the
beam.
If, as in Fig. 1.42, the steel rods in the bottom ofthe beam are. stretched and secured, this
would (without any external load) cause a compressive stress in the bottom and a small
tensile stress in the top ofthe beam. When an external force is applied, as in Fig. 1.43, the
entire cross section would then be. ~nd~r compression. This compression, through the entire
beam dept~, represents a better utthzat10n ofthe properties ofconcrete than
does the remforced concrete beam shown in Fig. 1.40
1.41 REINFORCED CONCRETE BEAM
1.42 POST-TENSION BEAM WITHOUT LOAD
1.43 POST-TENSION BEAM "WWTH LOAD

21. I'WITemmlheir §ii?2®§
Figure 1.44 illustrates the relative sizes ofbeams constructed! ofdifferent materials and
spanning a given distance with the same external load. These beams are drawn to the same
scale. The concrete and wood beams are similar in size while the steel beam is much
smaller.
Figure 1.45 shows typical columns ofvarious materials. These sketches represent columns
ofequal length and loading conditions. The wood and reinforced concrete columns are
similar in size while the steel column is smaller. The masonry pier m14st be several times
larger than the other columns.
I
l.44t RELATIVE SIZE OF BEAMS
. >:·: .· p. ·, ...
. 0 .. ~
.·. - ._,
·. . .... ·. ',
. .. ~ . ·.·. · ~.:
. . (. : . . .' .•
··y> . .... : .. : :·
. ·. @' ® ' 0-· '·
'>I · .. ·.
H
. : :· o . : D,: .·.· :
. ·". .. '® ·.
• ·.(I • . ·. -.- ~-
.?-. :~;·.,··.·~:--.··<>'
.::@ ·.: o.' ·, 10)_ '. ·•
::·. :_:... ~ -.. -... _·. <1 • • : .·
1.45 RELATIVE SIZE OF COLUMNS

22. (C((J)illldllll§ll@llD.
This chapter has illustrated that external forces or applied loads cause various types of
internal resistive forces and stresses. To obtain a stable structural system, these internal
forces must be resisted within the structure. The geometry and materials ofa structural
system determine the ability ofa structure to adequately resist external forces.
A keen observation of materials, form, and nature is helpful in obtaining an understanding
ofthe basic principles of structures. The principles and structural materials introduced in
. this chapter are very important to the understanding of structures.
The chapters which follow will be divided into two divisions: structural analysis and design
analysis which will deal with many structural forms used singly or in combination with
other forms to create architecture.
Jl. A force can be defined as that which tends to exert motion, compression or tension.
2. A compressive force tends to condense material.
3. A tensile force tends to stretch material.
4. A shearing force tends to divide an object along a plane parallel with the opposing
external forces.
5. Torque is the result of forces which tend to twist an object, resulting in a shearing stress.
6. Bending is the result of forces which tend to deflect a member by inducing tension,
compression and shear.
7. Internal forces cause stresses within structural members.
8. A moment may be defined as a force acting through a distance.

23. I
I
l··
I
.'..
: .
BEARING WALL
STRUCTURAL ANALYSIS
Introduction Abearing wall is a structural system that distributes loads which spread
gradually through a vertical or near vertical continuous mass to-supports. These loads
create internal compressive forces and stresses in the wall. -'
Examples ofthe bearing wall can be found in nature. One example is a 700 foot high
natural rock foundation~in Utah (Fig. 2.1). The rock formation is a result oferosion which
has not removed the more heavily stressed bearing material. The resulting formation is
wider at the base than at the top which distributes the accumulation ofloads over a larger
area and contributes to the stability oftlte fonnation.
Another example ofa bearing wall in nature is the Brazilian ant hill shown in Fig. 2.2. The
conical ant hill is constructed ofmany small .pieces. The increased width at the base ofthe
cone distributes the accumulation ofloads over a larger area and provides some natural
stability. The single exterior openingappears at the top where it does not disrupt the
structural continuity ofthe wall (Fig. 2.3).
: ·:.··
-.. ·'· .
: ' . ~
·
.:
.:<·;.. .
·:;{c .
·
..···
··
·
..
; .. .··
. . .·· . ,
i 2.1 ·· ~AfV~~;~q~t.ir~~~ATI?.~· -1)T~:~::··:
' .·

24. /
/
I
=.-: • •
··:.
Load Distributnolll
The distribution offorces in a bearing wall is similar to the distribution offorces in the
Brazilian ant hill and the natural rock formation. The weight ofthe wall increases toward
its base. Ifthe compressive stress (f= PIA) ofthe material is to remain approximately
constant, then the area must increase as the load increases; thus the wall must become
thicker toward the base. The resulting shape of the wall section, illustrated in Fig. 2.4,
resembles a triangle and is called a battered wall. This shape ofbearing wall is quite
common when constructed of weak compressive materials.'.
The increase in the width atthe base ofthe battered wall distributes the total weight ofthe
wall over large area ofsoil. As a result ofthis distribution, the weight ,ofthe wall does not
exceed the bearing capacity ofthe soil
Abearing wall is a compressive member that is continuous in one direction that distributes
vertical loads which spread gradually to the support (usually soil). It differs from a
continuous row ofadjacent columns in its ability to spread the load out along its length
(acting as abeam; Figure 7.7) and to provide inherent lateral resistance in the plane ofthe
wall (diaphragm: Figure 7.8). Both ofthese actions result from the internal shearing
stresses that can develop within the.wall.
Figure 7.7: A bearing wall spreads concentrated loads along its length as a
result of vertical shear resistance; the same load applied to a continuous
row of columns remains concentrated in a single column.
2.4 BATTEREn.
.STONE WALL
. .· .
:i / .
]
. •i :
Fi ure 7.8: A bearing wall provides lateral stability along it~ le~gth a~ a r~sutt;!i
' ofghorizontal shear resistance (diaphragm action); th1s IS lackmg tnj
continuous row of columns.
. . 1... .
2.5 VERTICAL BLOCK·WALL
i

25. A vertical bearing wall may be constructed with materials strong in compression (Fig2.5)..
The stress in this wall increases toward the base since the thickness ofthe wall does not
vary and the area remains constant. This type ofwall is not as stmcturally efficient as a
battered wall since the material in the top is not fully stressed.
The area ofthe base ofthis, wall is smaller than the battered wall, and the load ofthe wall
may exceed the bearing capacity ofthe soil. Increasing thearea.under the base ofthe wall
with a footing, as shown in Fig..5, will distribute the total weight ofthe wall over a larger
area ofsoil.
The distribution oflive and dead loads within the bearing wall can be illustrated with
several sketches.
Figure 2 6 illustrates typical forces acting on and within a bearing wall. For maximum
structural efficiency, joists or beams must be closely spaced to distribute the load evenly
throughout the entire wall. The triangular sha.ded areas on the el.evation ofthe wall
illustrate the approximate load distribution ofeach joist. This load distribution increases
uniformly from top to bottom thtoughout the entire wall. The uniform load distribution will
cause a gradual increase ofstress in the wall and a uniform stress on the footing and the
soil.
,.
Ifthe structural continuity is dismpted by a large opening as illustrated in Fig. 2.7, the
stress will not increase uniformly throughout the wall and the loads on the footing will not
be uniforms Notice the increase in load disttibution around the opening. This bearing wall
is less efficient than the wall illustrated in Fig. 2.6 since the loads are not transferred
directly and uniformly to the footing.
~ . . .. : ..;.·. :
. .
i _.
. i .
2.6 , STRESS INTYPICAL·BEAIUNG W~LL

26. Figure 2.8 shows a portion ofa bearing wall with the loads spaced at wider intervals than in 4
Fig. 2.6. The load distribution within the wall is not as uniform under this type ofloading..
The internal stresses va1y considerably near the top ofthe wall, but they are beginning to.
show some degree ofuniformity toward the base.
This type ofbearing wall is not as efficient in the distribution ofloads and resistance to
forces as is a wall with closely spaced loads.
When beams are widely spaced as shown in Fig. 2.9, heavy concentrated loads are
transferred to the wall These heavy loads may tend to crust! the wall below the beams.
Bearing plates are frequently used to distribute the concentrated load from the beams over a
larger wall area. This wjll reduce the concentration ofstresses on the top ofthe wall, as
shown in the sketch. A portion ofthe wall between supports is non-bearing. The stress near
the base ofthe wall will not be as uniform as Fig. 2.6 or 2.7 and the distribution ofthe load
to the footing will cause unequal stresses in the footing. The sketch shown in Fig. 2.9
demonstrated that a bearing wall under widely spaced concentrated loads is not an efficient
structural system. A m~)fe efficient use ofmaterial is obtained by increasing the wall
thickness beneath these concentrated loads, as illustrated in Fig. 2.10. These loads are
concentrated at points oflarger, area called pilasters. Less wall material can be used
between pilasters because the force is considerably less in the wall than in the pilasters. The
2.8 . BEAMS ON A BEARING WALL
:: : ·.. :. . ;
+
.. . .. .
,2.11 ,:STABILITY ~OF TRIANGLE ·.
.AND RECTANGLE . . . .
I
I
I
I
2.9 .· WIDELY SPACED BEAMS
ON A BEARING WALL
2·1° CONCENTRATED LOADS
ON .PILASTERS

27. I .
I
I
i
i
.,
'
tootmg ts also emargea unoer tne puasrer w equanze me mstnouuuu u 1 m't: tU(j-'J~ t.u t.ut: l!>UH
The wall between the pilasters is not required to carry more than its own weight and may
be considered a non-bearing wall. This type ofconstruction closely resembles the post and
beam system in which the loads are concentrated and carried to the ground through piers or
columns.
These examples indicate that the bearing wall is most efficient when
the loads are relatively uniform and closely spaced .along the entire length ofthe wall with
few, ifany, openings in the wall
LateraD Stability
In order for a bearing wall to fall over, the resultant ofall the lateral and ve1tical forces
must fall outside ofthe base ofthe wall. Ifthe development oftensile forces is to be
avoided (ifa masonry walJ is not reinforced), then the resultant ofall the lateral and vertical
forces must be further restricted to the middle third ofthe wall at any height.
Figure 2 11 compares the stability oftwo geometric forms the triangle and the rectangle
The cross sectional areas ofmost bearing walls are either rectangular or triangular. The
center ofweight ofthe triangle is clqser to its base than is the center ofweight ofthe
rectangle. This lower center ofgravity in the triangle makes it more resistive to overturning
than the rectangle. The broad base ofthe triangle also contributes to its stability.
The battered wall is an effective means ofdeveloping lateral stability with weak
compressive materials. A more efficient method ofdeveloping lateral stability should
considered when strong compressive materials are available.
Figure 2.12 illustrates a method ofobtaining lateral stability by the addition ofbuttresses to
a thin straight rectangular wall ofuniform thickness. Buttresses increase the stability ofthe
wall through the triangulation ofa portion ofthe wall. This method ofdeveloping stability
is not the most efficient. It requires the addition ofmore material than is necessary to
sustain the applied loads. The buttresses in this illustration stabilize the bearing wall
whereas the pilasters in Fig. 2.10 transfer concentrated loads to the footing.
The most efficient method ofdeveloping stability is through geometry instead ofmass.
This can be demonstrated with playing cards. Figure.
2.13 shows that two cards placed end to end forming a straight wall would not be stable
unless supported.
2.12. BUTTRE.SSED BEARIN,G WALL .
2.13 STABILITY OF THIN SECTION

28. Stability without additiOnal support IS pOSSIOte wntm t.WU '-41 u;:, cu... }''""'"'........... ·o··~ -··o·-..... •v
one another as shown in Fig 2 14 This method is employed to stabilize the bearing wall. (
Fig. 2.15) Fig. 2.16 shows the stability may be obtained with a single curved card .The
stability ofcard is increased as the radius ofcurve is decreased. The cylindrical and the
undulating walls shown in fig. 2.17 are examples of stable bearing walls.
These examples have shown how stability ofbearing walls can generally be obtained
through the careful use ofgeometry
A..
2.14 STABILIZED THIN SECTION
j ·
2.15 STABLE WALL
····~·..·
·· . . ; ·.
·•2.16···CURVED SECTION
. .
, .. ·. ···
···'" ..
.. . 11.~.....~ ~ '
'· .....
2.11 ' cv~vEn :
WALLs . I

29. DESIGN ANALY§liS
The design ofthe primitive shelter shown in Fig. 2.18 was an ingenious application ofbasic
structural principles using rubble stone. Combining wall and roofin a single form, acting as
both structure and space enclosure, this shelter developed natural stability through the
geometry, ofthe cone. The circular plan permitted the stones to.firmly bear against one
another as the diameter ofeach course decreased toward the top. The use ofthis crude
irregular material, assembled without mortar, depended upoh gravity for rigidity. The walls
increased in thickness toward the base, providing stability. Unlike the direct structural and
functional simplicity ofthe ant hill, this man-made structure demonstrates an example of
structural discontinuity through the introduction ofan opening at the base ofthe bearing
wall. The location ofan opening at a point ofheavy load concentration required a means of
diverting the weight ofthe wall above to either side ofthe opening. In this. example, the
huge stone lintel used to bridge the operung becomes the largest·single construction
element. Where large stones were not available, voids were often spanned by an arch or
corbel.
Temple ofhorus ,
The pylons ofthe Egyptian temple illustrate an example ofstability developed through
mass, employing the battered wall (Fig. 2.19). Forty feet thick at the base, the masonry
walls slope inward and upward to a height of 100 feet. The low center ofgravity and thick
base ofthis near- triangular mass effectively resist overturning The batter spreads the
enormous weight ofthe wall over a wide ground area at the base preventing undue
settlement ofthe structure. The batter. also spreads the weight over a larger wall area
toward the base.
This maintains the stress within the structural capacity ofthe wall material. The great
thickness and immense weight developed by the pylons limited the size ofopenings to very
small penetrations. These could be easily spanned with short stone lintels which caused a
minimum ofdisturbance in the vertical distribution ofloads.
B
... ·
:
.':. ; / .-
.:.. . . _·..
. • • -~ ........ !I' •••
·.· ,...... . .
: .·. . . .
2~18 .PRIMITIVE IJEARING WALL
· STRUCTURE TRULLI
..
u· ..
. . - .
2.19 PYLONS. TEMPLE OF HORUS:
EDFU. 237-57 B.C.

30. Medieval barn S
The Medieval bam shown in Fig 2 21 '11 t
wall by the addition ofbuttresse~ Am~reu! rates ~ m~thod ofdeve~oping stability in the
these buttresses provide mass at isolated of~~oa~~ca use ofmate~t~ls than batt~red walls,
several points ~tiffens ~he relat!vely high ~hin wall ~!dt~~;~~~s~~~~:~~;~:.~~t~~:ess at
~~~~etrr oftnangulattOn. W~lle the buttresses ofthe tall end wall provide resfstance to
exert~;~h!h~=b~~::o~~~:::o:~~:~sc~::ntra~~dloa~dsasbwell as resisting the thrust
non-bearing walls. een ese st e uttresses are essentially
.:n w
· . · , . . ' rum
··· .·
I I I . . .
· r : : :-:·:·: : :· : : : :
. . • .: . : : : : : .: :·.. f I ! . : : :
...•~. :::Iri H
·::.:;· .
·.
. ':. ,· .:: .. ~ .; . .
... ..··
~- . . ~. :· -· ' .'·
. -:- . .
.·
. :2.21 OLD TITHEBARN• ·
BRADFORD~oN:AVON•.· ·1350
Mission church
.. :I
. :2.23 MISSION:CHURCH. NEW MEXICO.
17th. CENTURY ·.
Figure 2.23 illustrates the influence ofmaterials upon the design ofa bearing wall in the
Southwestern United States. The design ofthis structure is influenced by the physical
properties ofadobe, a sun dried mud and-grass building block..
Thick battered walls provide stability and distribute loads over alarge area preventing the
weak structural material from being crushed under its own weight. The excessive mass of
thick walls is justified since it acts as insulation against the oppressive heat ofthe region.
The very close spacing ofthe projecting rooftimbers limits the load carried by each and
permit a uniform distribution ofthe roofloads, thus avoiding a concentration ofheavy
loads on the weak bearing material. The narrow openings are spanned with short exposed
lintels which express the distribution ofloads over these openings.

31. /
I
I
_J
/2.24. MONAIJNOC~ BUILDING·. CHICAGO. ground floor plan EfJ
. . BURNHAM arid.;ROOT~· ,1891 · ·
Monadnock building
The limitations ofthe masonry bearing wall as a structural system for multistory buildings
became evident in the Monadnock Building (Fig 2 24)
The massive walls which are sixteen stories high increase in thickness toward the base to
spread the load and prevent the brick from being crushed beneath the enormous
accumulation ofweight. The wall thickness is expressed by the deep openings. The vertical
alignment ofvoids and solids permits loads to be transferred directly to the ground.·The
bearing wall, when used in buildings ofgreat height, consumed a large portion offloor area
at the lower levels and limited the continued use ofthis structural system for multistory
buildings.
/!
i I
; j
!
I
I
I
/
. · r~. ...~-,;
[a··. a:
. I ·• D
...__ . ;~
·: -~~
.-...
. , .
. . :. :{·.. _:..
:.·;· .·
Unity temple
The reinforced concrete church shown in Fig 225 illustrates a method ofobtaining stability
in bearing walls through geometry. The strength ofreinforced concrete allows the
monolithic walls to be relatively thin. The walls, lacking the stability developed by mass,
have been turned 90 degrees at the comers to develop rigidity and to provide resistance to
overturning. Each independent segment offolded wall tends to develop its own stability.
Glass has been inserted between these segments to provide a limited quantity ofnatural
illumination, while emphasizing the structural independence ofeach segment. .-

32. I
!
•. L_
.
111111 IIIIIIli lllllllll
2.26 INTER-FAITH.CENTER~ BRANll:ElS
UNIVERSITY. ABRAMOVITZ. ·. .t9S5 ...
Interfaith center
Figure 2.26 illustrates an example ofstability resulting from the geometry ofthe curved
plane. Fired bricks, a strong compressive material ofuniform size and quality, have been
assembled to create two tall slender walls. These walls have been stabilized by the
geometry oftheir curvature rather than mass. This curvature resists the tendency ofthe
walls to overturn, thus preserving their narrow width and resulting in an economy of
material. The geometry of.the structure creates two large natural openings which do not
appreciably affect the structural continuity ofthe system.
SUMMARY- BEARING WALL
•v
1. Abearing wail is a supporting system constructed ofcompressive materials -
2 .It is most efficient when uniformly loaded.
3. Geometry is more efficient than mass in developing stability.
4. Openings within the waildisrupt the structural continuity ofthe system and should be
limited an size and number
.5.Natural openings exist between opposing pairs ofbearing, wails..
Jo

33. Ch.3
POST AND BEAM
Structauai AnaBysis
Introduction
The post and beam is a structural system which distributes loads to supports through a linear
arrangement of horizontal and vertical members. The vertical members are referred to as
posts or columns and resist primarily compressive forces. The horizontal members are
referred to as joists, beams, or girders, and resist bending forces and shear.
Posts are quite common in nature. Typical examples are the human leg, tree trunks, and
flower sterns. In contrast, the horizontal beam, and therefore the post and beam system, is
practically nonexistent in nature. There are many forms in nature which may resemble the
post and beam system; however, the beam form is curvilinear. These curvilinear beam forms
distribute loads by either tension or compression with little, ifany, bending.
The Banyon tree has a growth pattern which resembles the post and beam system (Fig. 3.1).
Long extended horizontal limbs are supported by vertical growth. These limbs carry their
own weight and are not intended to support large external loads or forces.
3.1 BANYAN TREE
Load Distribution
The most direct manner oftransferring loads through a post and beam system is usually the
most efficient and satisfactory method. The members ofthis system often reflect the
proportion ofload that they carry, as illustrated in the following examples.
1
When two loads of 150 pounds each are placed on a beam, equidistant from the center
support, the system is in equilibrium as illustrated in Fig. 3.2. The total load carried to the
ground is 300 pounds. If this system is inverted it would be similar to the post and beam
system shown in Fig. 3.3. One half ofthe concentrated load is transferred horizontally to each
end ofthe beam where it is transferred to the column and then vertically to the ground. The
columns support loads of 150 pounds each and are of equal size.

34. Figure 3.4 shows a beam with unequal loads placed (U1 unequal distance from the center
support. If the weight of the load multiplied by its distance from the support on one side is
equal to the weight of the load• multiplied by its distunce from the support on the other side,
the moments will be equal and the system will be in equilibrium If this system is inverted it
would be similar to the post and beam system shown in Fig 3 5 in which the concentrated
load of300 pounds is located near one end ofthe beam A greater portion ofthe load ~s
transferred horizontally to the left support in this example than is transferred to the right
support This unequal distribution of load supported by the columns is reflected in the
different column sizes
3.2 EQUILIBRIUM WITH EQUAL LOADS
3.3 EQUAL COLUMN LOADS
· 3.4 EQUILIBRIUM WITH UNEQUAL .LOADS
3.5 UNEQUAL COLUMN LOADS
A post-and-beam assembly works well for gravity loads. Under gravity loads, the beam is
subjed~'d'to bena1il,g;Because there is no connection between the post and the beam the
ben~t~~)p::ili.,~ ~b~@l .is p.ottr~ferreq to the post. Fig.2. Consequently, the P()Sts are under
P'¥:~:~~Rm~,t~-~I2~~,:~8/8~~~,~g.1 .. :,:: i _. . . . ···:<':~ ,.,. ,-,
,-:·.
• f,~~~z::~i~~~~~~~-~;:~.~~~~~~:~,$&s.~~1tJ~~f~!~~
1
~e
~~~?~i~~i~itil~~~;.···.··~~~i~~~?l~~~~1~;~~~[~$~00g)~·base,
~-~~~!!}~£{ag:~~;tH&~~~~~t~:~r~~y~~~t:kz{ft~~~s:t~~d
····.ill(ltllt~::~r~ti,l1~:~;:~~:
distri&litea~load. This tlJoriri'i'1b~'li~·fian~fffiea·ct.~iy'fb'~~l{'c~Hilliri'aiicf therefore the
oo1iU:tifls,8re the same size. Ifunequal'loads are distributed along a beam as shown in Fig. 3.7,
the;iJ.isfubution ofthe load to the columns is not equal, and the column sizes required indicate
this tu1equal distribution.

35. '"
Post Post
FIGURE 2 Under gravity loads, the
beam in a post-and-beam structure is
subjected to bending, which causes it to
rotate at the joint. Because of the
absence of a connection between the
post and the beam, the rotation of the
beam at the joint is not transferred to the
post. The post is, therefore, subjected to
compression only.
(=
=: -:..:.--~~------':.:.---------.:.:.::::::r:
---------------.,--11
' •'
' '
'
3
(a) Instability of a post-and-
beam structure under in-plane
lateral loads
(b) Instability of a post-and-beam
structure under out-of-plane
lateral loads
}?~:,:
}
;fiGURE 3 Under the action of both in-plane and out-of-plane lateral loads, a post-and-beam structure is unstab
t-:-~}.~·
! : '· ·;;
3.6 · UNIFORM LOAD ON BEAM
.. . .··.,
..3.7 "NON-UNIFORM BEAM LOAD
All ofthe vertical applied loads on the beam will be equal to the total load that the columns
must support and transfer to the ground. The summation of all vertical forces acting
downward must be equal to the summation of all the verticalresisting' forces acting upward
ifthe structure is to remain in equilibrium
A pictorial view ofa simple post and beam system is shown in Fig. 3.8. The two end frames
are similar to the frame shown in Fig. 3.3. When 1000 pounds is concentrated at mid-span on
the beam the load will be distributed throughout the entire system to the ground. One halfof
this total. load (500 pounds) is transferred from the beam to each frame. This 500 pound load
at the center ofthe frame beam is transferred equally to the columns. Each column supports
250 pounds. The central beam carries the greatest load in the system and is therefore larger
than either ofthe frame beams. Each ofthe columns supports the same load and is ofequal
stze.

36. 3.8
,' ·' ."
~ "
~ · · '··
..·. ·,
POST AND BEAM. SINGLE LOAD
3.9
·;'· . ' .......
POST AND BEAM. UNIF'dRM·:LQAD
Bays
A bay is an internal division of a repeating structural frame defined by the column (or bearing
wall) spacing. Simple structural bays consist of columns along all four sides ofthe structural
bays (Figure 9.15). while simple in appearance, this layout results in the columns in the
center having the greatest load (that of a full bay), side columns having Loads halfthat of
those in the center (half bays), and comer columns having loads only one-fourth that ofthe
center (quarter bays). To equalize the loading on all columns, half-bays can be created on the
perimeter by using overhanging beams. This equalizes the load on columns and reduces the
number ofcolurims required.
I I
r----0--~ ~ · M- --· r-- - - -· --·· -- ., r· ·· -- - --;-- - .,
I I
I
I I
I i I
I I • • • • • • ..I
I I I I I I
.. • • • I I I I
'
I I I
I
I I
I I
I I
• • • • I .
. • • I
I I I I
I I
I I I
I
• • • • I
I I I I
I I
I I I I
I
I • • • • I • • •
i I I I
I
• • • • I I
I I
I I
i• I
I
• ..
... • • • • I
I ,. I I I
) I I I i I
.. •· • ~ I I
I I I I
I I
... • .. .. • • I
.,. I I
I I I I I •
·----·--·--·-- --· L---- -- ______ J 1.- _ (_- ------- - - J
(a) : (b) (c.)
Figure 9.15 : Structural bays: (a) simple bays, 24 columns required; (b)
overhanging bays on two sides, 20 columns required; and (c) overhanging
bays on four sides, 15 columns required.
•.

37. The following examples illustrate how loads are distributed in multiple bay systems. 5'
Figure 3.10 shows two separate bays simil~ t? t~e bay of Fig. 3.9. Each bay may be divided
into four areas of equal size and weight. This 1s Illustrated by the shaded area on one bay.
Each beam carries a load of two areas or one half the total bay load. Each column supports
one half ofthe beam load which is the load of one area.
Figure 3.11 shows these two bays combined. In this system each ofthe four .be~piS·C"-rries
tWo areas as in the previous example. The six columns do not support equal loads and are
unequal in size. The end columns support only one are~ eac~, while the center colullli).S.
support two areas each. Two column sizes will be reqmred If they are to reflect the ver,ttcal
load that each column must support.
i
I
(
3.10 TWO SINGLE BAYS
3.11 TWO BAYS COMBINED
In Fig. 3.12 the two bays have been combined in another way which alters the distribution of
the loads from the previous example. The end beams still carry two areas. The center beam
carries four areas which require this beam to be larger than the end beams. The center ·
columns support two areas and are larger than the comer columns which• support one area
each. ··.· ·.· · ·
Two bays are shown)n Fig. 3.13, one placed upon the other. The total area load distribution
of~e top bay is similar to that discussed in example 3.10. The beams in the lower bay carry
the same areas those in the upper bay and are identical in size. The upper columns each
support one area The lower columns support the load from the upper columns as well as one
area from the lower barn, or a total oftwo areas. The lower columns are, therefore, larger
than the upper columns.
3.12 ALTERNATE COMBINATION
OF TWO BAYS ·-···· 3.13 TWO STACKED BAYS

38. A combinntion of four stacked bays is shown in Fig. 3.14. All ofthe beams in this ex;ampAe
carry the same load and are equal in size. The load distribution in the columns is not equal
Each center column in the top bays supports two areas, and the comer columns support one
area. The center columns in the lower bays support four areas, and the corner columns
suppoti.two areas. The various column sizes shown in this·figure reflect the loads which they
support.
The post and beam system may be expanded by the addition ofbays, bo1h horizontally and
vertically. The distribution ofloads throughout these multiple bay systems is reflected by the
various sized members which comprise these systems.
Column and beam sizes frequently remain unchanged even though the stresses within the
members may be unequal. This is often the result of other design considerations or the
economy of fabrication and construction.
3.14 FOUR STACKEI). BAYS
Lateral Stability •
R~fstanceio wind and'other·horiiontal forces 'is required fofthe'stability of orthogonal
fnfu1es. In general, t~isjs:a.qhiey~d by usingope ormore ofthefqllqwif1gprinciples:
'~;tf.iiifi-utationtbreruoit 'ffie.iframetdorh'Hito ti'ian.Ies whlch:iirle'lfiher:entl-·stable eometric
··;f6Ii1l~,.·Wi1J~ii~t»~:(~~llimg::~~gfaiS&nti(eet16n~li6f~'·m~ttiltets'(il)1et~~~)~.li!i& ~1e~r:watts
·ctHil~in'~,th~·-ttili;ent~~ifetliresistruictori·1
m13r~§ii'if~st~H:as ~~liir '·.·.to··c
han ''ii its
'"·;,sl{a:~·~,~~~is~t~e~~~dl':'1ilr:§tts~. " ··:,4~~:®~si~tafi~~:1~··~Ka~Mti1b~1f~t11§~t¢it~~Y?t,c.~i'st~1red
fu'r~iHe:;stability{of:Oftliogoh~frames.''ftfgenerat, tliisitadhievea·b~'Jisinfone)r moie'ofthe
fdi1'6Mtifil P.nncipies: trialigu1lltion (breaking the frame do~:mto trifuigl~:whlc
'h are .
.•• ·~t~...: ...!,·.. ~.. ..,., ~ • . :
inhere,pti~;stlible geometric forms ) joint rigidity (creating a,rigid corinection where members
int6r'S~9i)';;ana shear walls·(utilizing the inherent shear'resistance·errdplanar surface-such as
awall:.: its shape) (Figures 9.4 through 9.14).
. ' .·..... ·.··. •. ·.
.·
..· ' r~;l ; st~bility through triangulation: "Triangular frame is
Inherently stable with hinged joints. Recall that a triangle cannot chanoe
•. ) .· ,, ; o ' , . I o ...J
6 .

39. (a) (b)
(d) (e) (f)
Figure 9.5: Lateral stability through triangulation : (a) a rectangular frame is
inherently unstablewith hinged joints; (b) adding a diagonal cable tie provides
stability in one direction (when the cable is put in tension), (c) but not in the
other direction (the cable cannot resist compression); (d) adding a second
diagonal cable provides stability in both directions; (e) one diagonal strut
provides stability in both directions because it can resist both tension and
(f) compression.
Fi~u~e 9.6: Lateral stability is provided by cross-bracing expressed on the
bu1ld1ng ~xterior: John Hancock Center (1966; Chicago; Skidmore, Owings,
and Mernll , architects and engineers). The structure was conceived to allow
the sle~der building to resist the lateral wind loading. The architectural
express1on of the system was based on structural necessity.
Figure 9.7: Lateral stability through joint rigidity: Rigid top joints form a table.
Stability is achieved with one top rigid joint (which makes the frame behave
as a stable triangle). More than one rigid joint increases the frame's rigidity
but makes the system statically indeterminate.

40. Figure 9.9: Lateral stability through joint rigidity: Columns cantilevered from
the ground create rigid bottom joints. This system iscommonly ust-)d in "pole
barn" construction. Stability is achieved with one bottom rigid joint (which
makes the frame behave as a stable triangle). As above, more than one
rigid joint increases the frame's rigidity but makes the system statically
indeterminate.
equivalent
stable triangle
(b)

41. The simple post and beam system ofconstruction WiTi often laek natural lateral stability. .o/
Lateral forces, such as wind and earthquake, may cause structural failure unless they are
sufficiently restrained (fig. 3.15).
Methods ofstabilizing the post and beam structural system may vary considerably, but all are
designed to reduce or to el!mi11ate fue lateral displacement of the members within the
strUctural system.
A table with poorly connected legs is similar to an unrestrained post and beam system (Fig.
3.16). A horizontal. force applied to this table will reveal its instability. The table can be
stabilizedby fastening "beams" to the legs as shown in Fig. 3.17. Figure 3.18 shows a beam
and column system in which the beam has been rigidly connected to the column to produce a
rigid frame and reduce lateral instability. The columns are able to resist lo+~- ' ·' -
beam action or bendmg.
3.15 LATERAL INSTABILITY
3.17 · STABLE
3.16 UNSTABLE
r". :I~ ..·
Y!~
. ~~'--<7 .·
.. ::
3.18 STABILITY THROUGH RIGID JOINTING
Several additional methods ofobtaining lateral stability in post and beam systems are shown
in the following examples.
The diagonal tie rod is illustrated in Fig. 3.19. It transfers lateral forces through tension to
supports without producing bending in the columns.
./----. W
hen using cable bracing, two are necessary tostabilize the
3.19 DIAGONAL TIE RODS
structureagainst lateral forces from either direction. For
eachdirection, one cable w
illoperate effectivelyin tension
while the other wouldsimply buckle.lfrigid bracing is used,a
certain degree of redundancy is involved because asingle
member is capableofstabilizingthe structure.

42. The diagonal knee brace is shown in Fig. 3.20. The knee brace is similar to the tie rod and
does impart bending to the column from lateral forces.
(a) 1<.-brace profile (d) Eccentric 1<.-brace profile
3.20 KNEE ·BRACES
Masonry or other structural materials placed between the colwnns as illustrated in Fig. 3.21
acts as atwo-dimensional shear wall which will prevent lateral movement
A rigid reinforced concrete shear wall may be used as a three-dimensional anchor for the
skeleton frame (Fig. 3.22). This wall provides lateral stability without causing bending in the
columns.
Lateral stability in a structural system must be developed through out the entire system.
3.21 MASONRY INFILL
(a) Single brace
· FIGURE :q '.. )~) Jfa single brace is
used 'it mu§tbe sufficiently heavy
I '
against buckling under compression.
(b) Shear wall bracing.
3.22 CONCRETE SHEAR WALL
. .

43. .. '
DESIGN ANAJLYSIS
The structural principles e:xJribited by the primitive post and beam shelter of Fig. 3.23 remain
basically unchanged in contemporary architecture.The limited technology ofearly man,
however, severely restricted the size ofhis post and beam constructions. Pririlitive techniques
ofshaping and securely joining the structural members limited the construction to Jight
wooden poles which were usually lashed together to provide a structural skeietori oforuy
modest size. Lateral stability was developed by setting the four posts in the ground. Unlike
the bearing wa11, the supporting elements ofthis post and beam constm~tion produce only a
negligible amount ofshelter. Therefore, non-bearing space enclosing smfaces such as roof
and walls must be added to complete the shelter.
'
/
PRIMITlVE POST AND BEAM SHELTER
3.23
Th~ Greek temple (Fig. 3.24) is a classic expression of the post and beam system of ·
construction. Its fonn and proportions are significantlyinfluenced by the stmctural
limitations of stone, the building material. Restricted in span by the weakness ofstone in
bending, the deep lintels rest on massive, closely spaced columns producing atall narrow
proportion which became characteristic ofthe stone post and beam architecture of antiquity.
The circular cross-section ofthe column produced an efficient structural form. It developed
stability through its enormous width and mass.
THE THESEION. ATHENS. 449-444 B.C.
3.24

44. The building shown in Fig. 3.27 illustrates the freedom of planning possible within a large 1
'2.·
volume 1hat is unobstructed by columns. The basic stmcture and Joad distribution is
expressed by four large exposed girders and eight columns. The smaller columns support the
glass facade. The benefits of unobstructed space have been obtained at the expense of a
large, heavy framing system. Elimination of interior supports provides unlimited
opportunity for subdivision with non-bearing prutitions.
[[
' '
' '
' '
' '
' I
' '
o I
I '
' :
I '
' '
I o'
.: t:J
3.27 CROWN HALL. I.I.T.
MIES VAN DER ROHE. 1952
Figure 3.28 diagrrunatically illustrates the early development ofthe post and beam
skyscraper. Limitations in the continued use ofbearing walls became evident as taller
structures were attempted. For example, thick walls (a) which were required to sustain the
load, threatened to consume the useable floor area at lower levels. Useable floor area and
fl~bility were significantly incr:ef!Seq;bythereplacing ofthe interior bearing walls (b) with a
system ofcast!iro~tc(jlqn$;arid;:!Wi~I1gfit#oh :beams.':Stabilit.Y·w·
as'developed tlitough the
·j,- ' - ........:.;.. -· • ".-·~- .•:·:;:..,-.. .,,_,.___ ·t,·, ·;'•-~f'..<;'·'·-~···.r:·'''-:'-~·-·""'/ _-·~'-''..!_~ ;~''f--:"1:4,' ._....~.-- ' -. ·:·--.~-~.. _;t, ·~-- - ' . -._-. -.. - ·• '' .·- ~
thick bear,iri,g w,all$-ret~n~g_:·~t;f.ll¢·.:n;~m.~ter-;6f:the"p1$;;,·1fhe devel9pment:orthe'
·--·:· :,..._.."-'--:A,-,.,,,., '· ,..,,.,.,,-.,,_
_.~. ~ _.-_ --~· ; ~'-'t:.-Y!·..'t-.if:~ ..'""_:'-:!<i-.;..~~--~~·.-..~ .. •:_---..r..,-:-·'-,,~·~...... -_-.. -··•--._· . ·· j· .. • ~ ,~
cqrltemporary s.Icyscraper·enieiged;m])en:itli~£6uter~~~at.ing walls1
(¢) were replaced by beams
~~a~,,~91rul)ns~~ovid1ng.a~com~I~)~k~~tqil·di-ame'dr:~wcmrru':steeF: '·
• "' . ~-- •• ~.... '""j ....
! '••'· •
.... !. .~J. _... ,. ... ~
b
• •
• •
• •
c
. . .. ; . . . .
3.28 GUARANTY BUILDING. BUFFALO.
SULLIVAN. ·189$ •

45. . ,.
" .
A notable variation in high-rise structures is fund in the impressive 100 story John Hancock 13
Center (Fig. 331).
Its tapered outer walls and clearly expressed diagonal bracing made this a most unusual
solution at the time it was built The structural steel frame derives its strength and lateral
·siahility from the geometry ofthe complex ofdiagonal, horizontal and vertical members
joined with non-rigid connections The combination of these features reduced the amount of
steel by 30-40% compared with that required for the conventional skeleton frame
skyscraper which must develop much of its lateral stability through rigid joints.
The structural design of this building would have been virtually impossible without the aid of
sophisticated computations made possible by today's computer technology.
-
3.:31 JOHN HANCOCK CENTER. CHICAGO.
SKIDMORE, OWINGS and MERRILL. · d968

46. .-, ,¢:.:,,: ..: ·
.~ . .
SUMMAR' - POST nnd llf..IEAM
1The post and beam system is composed of horizontal and vertical members subject to
bending and compressive forces
2. Frames distribute loads horizontully (by means of beams or slabs) to columns (or beating
walls) which transmit the forces vertically to the supporting foundation.
3. Lateral stability in frames may be provided by triangulation ,joint rigidity, or shear walls.
4. A bay is an internal division of a repeating structural frame defined by the column (or
beruing wall) spacing.
5. The size of the structural units may vary depending upon the forces they must sustain
6. Lateral stability is not geometrically inherent in this rectangular system
7. Nonstructural elements are necessary for a complete space enclosure
8. The system suggests a modular arrangement ofboth structural and non- structural elements
6 The structural module may expand both horizontally and verticaJiy
9. The system is most appropriate for functions which do .not require large unobstructed
spaces.
10. The subdivision of space may be iildep.en~ent ofthe structuraJ system
11. Openings in a modular system do not disrupt the structmal continuity of the system.
"''
.;.
; ·-
( L --..