IS800-8Beam as a civil definition of design

Dr S R Satish Kumar, IIT Madras 1
IS 800:2007 Section 8
Design of members
subjected to bending

SECTION 8 DESIGN OF MEMBERS SUBJECTED TO BENDING
8.1 General
8.2 Design Strength in Bending (Flexure)
8.2.1 Laterally Supported Beam
8.2.2 Laterally Unsupported Beams
8.3 Effective Length of Compression Flanges
8.4 Shear
-------------------------------------------------------------------------------------------------
8.5 Stiffened Web Panels
8.5.1 End Panels design
8.5.2 End Panels designed using Tension field action
8.5.3 Anchor forces
8.6 Design of Beams and Plate Girders with Solid Webs
8.6.1 Minimum Web Thickness
8.6.2 Sectional Properties
8.6.3 Flanges Cont...

SECTION 8 DESIGN OF MEMBERS SUBJECTED TO BENDING
8.7 Stiffener Design
8.7.1 General
8.7.2 Design of Intermediate Transverse Web Stiffeners
8.7.3 Load carrying stiffeners
8.7.4 Bearing Stiffeners
8.7.5 Design of Load Carrying Stiffeners
8.7.6 Design of Bearing Stiffeners
8.7.7 Design of Diagonal Stiffeners
8.7.8 Design of Tension Stiffeners
8.7.9 Torsional Stiffeners
8.7.10 Connection to Web of Load Carrying and Bearing Stiffeners
8.7.11 Connection to Flanges
8.7.12 Hollow Sections
8.8 Box Girders
8.9 Purlins and sheeting rails (girts)
8.10 Bending in a Non-Principal Plane

• Plastic hinge formation
• Lateral deflection and twist
• Local buckling of
i) Flange in compression
ii) Web due to shear
iii) Web in compression due to
concentrated loads
• Local failure by
i) Yield of web by shear
ii) Crushing of web
iii) Buckling of thin flanges
RESPONSE OF BEAMS TO VERTICAL LOADING

LOCAL BUCKLING AND SECTION CLASSIFICATION
OPEN AND CLOSED SECTIONS
Strength of compression members depends on slenderness ratio

(b)
(a)
Local buckling of Compression Members
LOCAL BUCKLING
Beams – compression flange buckles locally
Fabricated and cold-formed sections prone to local buckling
Local buckling gives distortion of c/s but need not lead to collapse

L
Bending Moment Diagram
Plastic hinges
Mp
Collapse mechanism
Plastic hinges
Mp
Formation of a Collapse Mechanism in a Fixed Beam
w
Bending Moment Diagram
BASIC CONCEPTS OF PLASTIC THEORY
First yield moment My
Plastic moment Mp
Shape factor S = Mp/My
Rotation Capacity (a) at My(b) My < M<Mp
(c) at Mp
Plastification of Cross-section under Bending

SECTION CLASSIFICATION
Mp
Rotation 
My
y u
Slender
Semi-compact
Compact
Plastic
Section Classification based on Moment-Rotation Characteristics

Moment Capacities of Sections
My
Mp
1 2 3 =b/t
Semi-
Compact Slender
Plastic Compact
SECTION CLASSIFICATION BASED ON
WIDTH -THICKNESS RATIO
For Compression members use compact or plastic sections

Type of Element Type of
Section
Class of Section
Plastic (1) Compact
(2)
Semi-compact (3)
Outstand element of
compression flange
Rolled b/t  9.4 b/t  10.5 b/t  15.7
Welded b/t  8.4 b/t  9.4 b/t  13.6
Internal element of
compression flange
bending b/t  29.3 b/t  33.5 b/t  42
Axial
comp.
not applicable b/t  42
Web NA at mid
depth
d/t  84.0 d/t  105 d/t  126
Angles bending
Axial
comp.
Circular tube with
outer diameter D
D/t  442 D/t  632 D/t  882
Table 2 Limits on Width to Thickness Ratio of Plate Elements
y
f
250


b/t  9.4 b/t  10.5 b/t  15.7
not applicable b/t  15.7
(b+d)/t  25

Condition for Beam Lateral Stability
• 1 Laterally Supported Beam
The design bending strength of beams, adequately
supported against lateral torsional buckling (laterally
supported beam) is governed by the yield stress
• 2 Laterally Unsupported Beams
When a beam is not adequately supported against lateral
buckling (laterally un-supported beams) the design
bending strength may be governed by lateral torsional
buckling strength

Design Strength in Bending (Flexure)
The factored design moment, M at any section, in a beam due to
external actions shall satisfy
Type 1 Sections with stocky webs
d / tw  67
The design bending strength as governed by plastic strength, Md,
shall be found without Shear Interaction for low shear case
represented by
V <0.6 Vd
d
M
M 

• V exceeds 0.6Vd
Md = Mdv
Mdv= design bending strength under high
shear as defined in section 9.2
8.2.1.3 Design Bending Strength under High Shear

Definition of Yield and Plastic Moment Capacities

8.2 Design Strength in Bending (Flexure)
The factored design moment, M at any section, in a beam
due to
external actions shall satisfy
The design bending strength as governed by plastic
strength, Md, shall be taken as
Md = b Z p fy / m0  1.2 Ze fy / m0
8.2.1.4 Holes in the tension zone
(Anf / Agf)  (fy/fu) (m1 / m0 ) / 0.9
d
M
M 

Laterally Stability of Beams

BEHAVIOUR OF MEMBERS SUBJECTED TO
BENDING
Plastic
Range
Inelastic
Range
Elastic
Range
Mp
My
Mcr
Unbraced Length, L
Mo Mo
L
Beam Buckling Behaviour

LATERAL BUCKLING OF BEAMS
 FACTORS TO BE CONSIDERED
 Distance between lateral supports to the compression
flange.
 Restraints at the ends and at intermediate support
locations (boundary conditions).
 Type and position of the loads.
 Moment gradient along the unsupported length.
 Type of cross-section.
 Non-prismatic nature of the member.
 Material properties.
 Magnitude and distribution of residual stresses.
 Initial imperfections of geometry and eccentricity of
loading.

SIMILARITY BETWEEN COLUMN BUCKLING
AND LATERAL BUCKLING OF BEAMS
Column Beam
Short span Axial
compression
& attainment
of squash load
Bending in the plane of
loads and attaining
plastic capacity
Long span Initial
shortening
and lateral
buckling
Initial vertical deflection
and lateral torsional
buckling
Pure flexural mode
Function of slenderness
Coupled lateral
deflection and twist
function of slenderness
Both have tendency to fail by buckling in their weaker plane

Beam buckling
EIx >EIy
EIx >GJ
SIMILARITY OF COLUMN BUCKLING AND BEAM BUCKLING -1
M

u
M
Section B-B
u
P
P
Section B-B
B
B B
B
Y
X
Z
Column buckling
3
l
y
EI
l
EA


LATERAL TORSIONAL BUCKLING OF
SYMMETRIC SECTIONS
Assumptions for the ideal (basic) case
• Beam undistorted
• Elastic behaviour
• Loading by equal and opposite moments in the
plane of the web
• No residual stresses
• Ends are simply supported vertically and laterally
The bending moment at which a beam fails by
lateral buckling when subjected to uniform end
moment is called its elastic critical moment (Mcr)

(a) ORIGINAL BEAM (b) LATERALLY BUCKLED BEAM
M
Plan
Elevation
l
M
Section
(a)
θ
Lateral
Deflection
y
z
(b)
Twisting
x
A
A
Section A-A

Mcr = [ (Torsional resistance )2 + (Warping resistance )2 ]1/2
 
2
1
2
y
2
y
cr
L
Γ
I
E
Π
J
G
I
E
L
Π
M















 







 
2
1
2
2
2
1
y
cr
J
G
L
Γ
E
Π
1
J
G
I
E
L
Π
M 






















or
EIy = flexural rigidity
GJ = torsional rigidity
E = warping rigidity

FACTORS AFFECTING LATERAL STABILITY
• Support Conditions
• effective (unsupported) length
• Level of load application
• stabilizing or destabilizing ?
• Type of loading
• Uniform or moment gradient ?
• Shape of cross-section
• open or closed section ?

EQUIVALENT UNIFORM MOMENT FACTOR (m)
Elastic instability at M’ = m Mmax (m  1)
m = 0.57+ 0.33ß + 0.1ß2 > 0.43
ß = Mmin / Mmax (-1.0  ß  1.0)
Mmin
Mmax
Mmin
Positive
Mmax Mmin
Mmin
Negative
Mmax
Mmax
also check Mmax  Mp

8.2.2 Laterally Unsupported Beams
The design bending strength of laterally unsupported beam
is given by:
Md = b Zp fbd
fbd = design stress in bending, obtained as ,fbd = LT fy /γm0
LT = reduction factor to account for lateral torsional
buckling given by:
LT = 0.21 for rolled section,
LT = 0.49 for welded section
Cont…
 
0
.
1
]
[
1
5
.
0
2
2




LT
LT
LT
LT




 
 
2
2
.
0
1
5
.
0 LT
LT
LT
LT 


 



cr
y
p
b
LT M
f
Z /

 

8.2.2.1 Elastic Lateral Torsional Buckling Moment
    
























 2
2
2
2
KL
EI
GI
KL
EI
M w
t
y
cr


5
.
0
2
2
2
/
/
20
1
1
)
(
2 

















f
y
y
LT
cr
t
h
r
KL
KL
h
EI
M


APPENDIX F ELASTIC LATERAL TORSIONAL BUCKLING
F.1 Elastic Critical Moment
F.1.1 Basic
F.1.2 Elastic Critical Moment of a Section Symmetrical about
Minor Axis

EFFECTIVE LATERAL RESTRAINT
Provision of proper lateral bracing improves lateral stability
Discrete and continuous bracing
Cross sectional distortion in the hogging moment region
Discrete bracing
• Level of attachment to the beam
• Level of application of the transverse load
• Type of connection
Properties of the beams
• Bracing should be of sufficient stiffness to produce
buckling between braces
• Sufficient strength to withstand force transformed by
beam before connecting

Effective bracing if they can resist not less than
1) 1% of the maximum force in the compression flange
2) Couple with lever arm distance between the flange
centroid and force not less than 1% of compression
flange force.
Temporary bracing
BRACING REQUIREMENTS

Other Failure Modes
Shear yielding near support
Web buckling Web crippling

Web Buckling
450
d / 2
d / 2 b1 n1
Effective width for web buckling
c
f
t
)
1
n
1
b
(
wb
P 

t
d
5
.
2
t
3
2
d
7
.
0
y
r
E
L
3
2
t
t
12
3
t
A
y
I
y
r
y
r
d
7
.
0
y
r
E
L









Web Crippling
b1 n2
1:2.5 slope
Root
radius
Stiff bearing length
yw
f
t
)
2
n
1
b
(
crip
P 


SUMMARY
• Unrestrained beams , loaded in their stiffer planes may undergo
lateral torsional buckling
• The prime factors that influence the buckling strength of beams
are unbraced span, Cross sectional shape, Type of end restraint
and Distribution of moment
• A simplified design approach has been presented
• Behaviour of real beams, cantilever and continuous beams
was described.
• Cases of mono symmetric beams , non uniform beams and
beams with unsymmetric sections were also discussed.

IS800-8Beam as a civil definition of design

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