Steel Structures - Design and Practice

460 Pages·2011·22.01 MB·English

by  Subramanian

Steel
Structures
Design and Practice
N. SUBRAMANIAN
Consulting Engineer
Maryland
USA
OXFORD
UNTVERS ITY I’RE S S
OXFORD
UNIVERSITY PRESS
YMCA Library Building,J ai Singh Road, New Delhi 110001
Oxford University Press is a department of the University of Oxford.
It furthers the University's objective of excellence in research, scholarship,
and education by publishing worldwide in
Oxford New York
Auckland Cape Town Dar es Salaam Hong Kong Karachi
Kuala Lumpur Madrid Melbourne Mexico City Nairobi
New Delhi Shanghai Taipei Toronto
With offices in
Argentina Austria Brazil. Chile Czech Republic France Greece
Guatemala Hungary Italy Japan Poland Portugal Singapore
South Korea Switzerland Thailand Turkey Ukraine Vietnam
Oxford is a registered trade mark of Oxford University Press
in the UK and in certain other countries.
Published in India
by Oxford University Press
0 Oxford University Press 2010
The moral rights of the author have been asserted.
Database right Oxford University Press (maker)
First published 2010
All rights reserved. No part of this publication may be reproduced,
stored in a retrieval system, or transmitted, in any form or by any means,
without the prior permission in writing of Oxford University Press,
or as expressly permitted by law, or under terms agreed with the appropriate
reprographics rights organization. Enquiries concerning reproduction
outside the scope of the above should be sent to the Rights Department.
Oxford University Press, at the address above.
You must not circulate this book in any other binding or cover
and you must impose this same condition on any acquirer.
ISBN-13: 978-0-19-806881-5
ISBN-10: 0-19-806881-6
'Qpeset in Times
by Pee-Gee Graphics, New Delhi
Printed in India by Chaman Enterprises, Delhi 110002
and published by Oxford University Press
YMCA Library Building, Jai Singh Road, New Delhi 110001
List of Symbols
A area of cross section; surface area A,, net sectional area of outstanding
of cladding 1%
A, area of bolt; gross area of horizon- A, initial cross-sectional area of ten-
tal boundary elements in SPSW sile test coupon
Abr required bearing area A, cross-sectional area of the stiffener
in contact with the flange
A, minor diameter area of the bolt;
gross area of vertical boundary elements A, tensile stress area
in SPSW A,, shank gross cross sectional area
(nominal area) of a bolt
A, area of diagonal member
A, area of stiffener
A, effective cross-sectionala rea; effec-
A, total area of the compartment in fire
tive frontal area in wind
gross sectional area in tension from
A, moment amplification factor A,,
the centre of the hole to the toe of the
total flange area of the smaller con-
As angle perpendicular to the line of force
nected column; floor area; required area
(block shear failure)
of flange plates
A,, net sectional area in tension from
A, gross cross-sectional area
the centre of the hole to the toe of the
A,, gross cross-sectional area of flange angle perpendicular to the line of force
gross cross sectional area of out-
A,, (block shear failure)
standing leg
A, sheararea
A, design horizontal seismic coeffi-
gross cross sectional area in shear
A,,
cient along the line of transmitted force (block
A, design horizontal acceleration spec- shear failure)
trum value of mode k
A,, net cross sectional area in shear
A, net area of the total cross section along the line of transmitted force (block
A,, net tensile cross sectional area of shear failure)
bolt A, effective cross-sectional area of
A,, net cross sectional area of the con- weld; window area; effective area of
nected leg walls; area of web
A,, effective net area a, b larger and smaller projection of
A,, net cross sectional area of each the slab base beyond the rectangle con-
flange sidering the column, respectively
xvi Design of Steel Structures
a, peak acceleration C, specific heat of steel
a, unsupported length of individual C, cost of truss
elements being laced between lacing c, moment reduction factor for lateral
points torsional buckling strength calculation
B breadth of flange of I-section; length D overall deptwdiameter of the cross
of side of cap or base plate of a column section
B, background factor 0, outer diameter
b, outstand/width of the element d depth of web; nominal diameter;
b, stiff bearing length; stiffener bear- grain size of crystals; diagonal length;
ing length depth of snow; base dimension of the
be effective width of flange between building
pair of bolts d2 twice the clear distance from the
b, width of column flange compression flange angles, plates, or
breadth or width of the flange tongue plates to the neutral axis
bf
panel zone width between column d, depth of angle
bp
flanges at beam column junction db beam depth; diameter of bolt
b, shear lag distance; stiffener width d, column depth
b,, average breadth of the structure dg centre-to-centre of the outermost
between heights s and h bolt of the end plate connection
b,, average breadth of the structure d, diameter of the hole
between heights 0 and h di thickness of insulation
b, width of tension field do nominal diameter of the pipe col-
b, width of outstanding leg umn or the dimensions of the column in
C centre-to-centre longitudinal dis- the depth direction of the base plate
tance of battens; coefficient related to dp panel zone depth in the beam-col-
thermal properties of wall, floor, etc.; umn junction
spacing of transverse stiffener; moisture E modulus of elasticity for steel; en-
content of insulation ergy released by earthquake
C, equivalent uniform moment factor E(r) modulus of elasticity of steel at
Cdyn dynamic response factor TOC
C, effective width of interior patch E(20) modulus of elasticity of steel at
load 2O0C
C> frictional drag coefficient E, equivalent elastic modulus of rope
Cf force coefficient of the structure EL, earthquake load in x direction
C,, cross-wind force spectrum coeffi- EL,, earthquake load in y direction
cient Ep modulus of elasticity of the panel
Ci specific heat of insulation material material
C,, lateral horizontal load for cranes Esh strain-hardening modulus
C, coefficient of thermal expansion; E, tangent modulus of elasticity
equivalent moment factor E’, reduced tangent modulus
Cp cost of purlin e eccentricity, head diagonal of bolt
Cpe external pressure coeficient eb edge distance of bolt
Cpi internal pressure coefficient F net wind force on cladding
C, cost of roof covering F’ frictional drag force
List of Symbols xvii
Fbr strength of lateral bracing ffm, highest normal stress range
F,, flange contribution factor ff, normal fatigue stress range for 5 x
F, minimum bolt pretension lo6 cycles
Fbsd bearing strength of stiffener fk characteristic strength
Fq stiffener force J; fatigue limit
fL
Fqd design buckling resistance of stiff- stress range at cut-off limit
ener f, mean stress
F,,, protection material density factor; fm, maximum stress
ultimate web crippling load fmin minimum stress
Fxd design resistance of load carrying f, proofstress
web stiffener fo first mode natural frequency of vi-
F, external load; force or reaction on bration of a structure in the along-wind
stiffener direction
F, along-wind equivalent static load at fo,2 0.2% proof stress
height Z fpl steel stress at proportional limit
f4
f actual normal stress range for the shear stress
detail category, uniaxial stress, fre- f R characteristic value of fatigue
quency of vortex shedding strength at loading cycle NR
fi, f2, f3 principal stresses acting in f,, shear stress due to torsion
three mutually perpendicular directions f,,w arping shear stress
f, stress amplitude J1 tension field strength
fb actual bending stress; bending stress f, characteristic ultimate tensile stress
at service load f,b characteristic ultimate tensile stress
fbc actual bending stress in compres- of the bolt
sion A,, characteristic ultimate tensile stress
fbd design bending compressive stress of the connected plate
corresponding to lateral buckling f,, ultimate tensile stress of the weld
fbt actual bending stress in tension at f, yield strength in the panel utilizing
service load tension field action
f, average axial compressive stress f,d design strength of weld
f,,,f,, elastic buckling stress of a col- fy characteristic yield stress
umn or plate; Euler’s buckling stress = yield stress of steel at TOC
&(T)
$E/(KL/r)2
fy(20) yield stress of steel at 2OoC
fck
characteristicc ompressive strength
fyb characteristic yield stress of bolt
of concrete
fy, characteristic yield stress of flange
f,, b extreme fibre compressive elastic fyn nominal yield strength
lateral buckling stress
fyst design yield stress of stiffener
fcd design compressive stress fyp characteristic yield stress of con-
fd stress range at constant amplitude
nected plate
f, equivalent stress
fy4 characteristic yield stress of stiff-
$- fatigue strength corresponding to N,,
ener material
cycle of loading
fy, characteristic yield stress of the
ffd design normal fatigue strength
web material
ff,,e quivalent constant amplitude
fo yield strength of very large isolated
stress range
crystals
xviii Design of Steel Structures
G shear modulus of rigidity for steel; I, second moment of inertia of stiff-
thickness of grout ener
G, gust factor Zt St. Venant's torsional constant
G* design dead load I, warping constant
g gauge length between the centre of 'y moment of inertia about the minor
the holes perpendicular to the load di- axis
rection; acceleration due to gravity; gap I, moment of inertia about the major
for clearance and tolerance axis
IF interference factor
g, peak factor for resonant response
H height of section; transverse load K effective length factor
Hp heated perimeter K, area averaging factor
H, calorific value of the vth combus- Kb effective stiffness of the beam and
tible material column; effective length factor for
H, window height beams against lateral bending
h depth of the section; storey height K, combination factor; stiffness of
column
hb total height from the base to the
floor level concerned Kd wind directionality factor
h, height of the column Kh reduction factor to account for the
he effective thickness bolt holes in HSFG connection
KL effective length of the member
he, embedment length of anchor bolt
h, distance between flange centroids KLIr appropriate effective slenderness
of I-section ratio of the section
h, thickness of protection material; KLIry effective slenderness ratio of the
height of floor i section about the minor axis
h, height of the lip KLIr, effectives lenderness ratio of the
h, storey height section about the major axis
(KLIr), actual maximum effective
hy distance between shear centre of the
two flanges of the cross section slenderness ratio of the laced or bat-
Z moment of the inertia of the member tened column
about an axis perpendicular to the plane (KLIr), effective slenderness ratio of
of the frame; impact factor fraction; im- the laced column accounting for shear
portance factor deformation
zb moment of inertia of brace K, mode share correction factor for
$ second moment of area of the foun- cross-wind acceleration
dation pad; insulation factor K,K, moment amplification factor
about respective axes
Zfc moment of inertia of the compres-
sion flange K, warping restraint factor
k regression coefficient; constant;
Zft moment of inertia of the tension
flange mode shape power exponent for the fun-
zh turbulence intensity at height h damental mode of vibration
'p polar moment of inertia k, probability factor or risk coefficient
Zq moment of inertia of a pair of stiff- k2 terrain, height and structure size
ener about the centre of the web, or a factor
single stiffener about the face of the web k3 topography factor
List of Symbols xix
k4 importance factor for cyclonic re- I,, distance from bolt centre line to the
gion toe of the fillet weld or to half the root
kb, kb, stiffness of bracing radius for a rolled section
k, modulus of sub-grade reaction M bending moment; magnitude of
k,,, web distortional stiffness earthquake
k,,,, exposed surface area to mass ra- Mlsway maximum first order end mo-
tio ment as a result of sway
k, brace stiffness excluding web dis- Mbr required flexural strength of tor-
tortion, torsion parameter sional bracing
ktb stiffness of torsional bracing M,, elastic critical moment corre-
k,, shear buckling coefficient sponding to lateral torsional buckling
L actual length; unsupported length; Md design flexural or bending strength
centre-to-centre distance of the intersect- Mdv design bending strength of the
ing members; length of the end connec- section under high shear
tion; cantilever length; land in weld design bending strength as gov-
Mdy
Lb laterally unbraced length or dis- erned by overall buckling about minor
tance between braces axis
L, length of end connection measured MdZ design bending strength as gov-
from the centre of the first bolt hole to erned by overall buckling about major
the centre of the last bolt hole in the con- axis
nection; distance between gantry gird- Me, reduced effective moment
ers Mf, reduced plastic moment capacity
L,, clear distance between flanges of of the flange plate
vertical boundary elements Mfd design plastic resistance of the
L, effective horizontal crest length flange alone
L, gauge length of tensile test coupon Mnd design strength under combined
L, measure of the integral turbulence axial force (uni-axial moment acting
length scale at height h alone)
L, maximum distance from the re- MndyM, ndz design strength under com-
straint at plastic hinge to an adjacent
bined axial force and the respective uni-
restraint (limiting distance)
axial moment acting alone
Lo length between points of zero mo- Mo cross-wind base overturning mo-
ment (inflection) in the span
ment; first order elastic moment
L, effective length of weld; length of
plastic moment capacity of the sec-
Mp
wall
tion
1, length of the angle
moment in the beam at the inter-
Mpb
1, distance between prying force and
section of the beam and column centre
bolt centre line
lines
lg grip length of connection
4 length of the joint Mpc moments in the column above and
below the beam surfaces
1, length between points of lateral sup-
Mpd plastic design strength
Port
plastic design strength of flanges
1, elongation due to temperature; Mpf
only
length of top angle
xx Design of Steel Structures
Mpr reduced plastic moment P factored applied axial force; point
capacity of the section due to axial force load
or shear Pbf design strength of column web to
Mq applied moment on the stiffener resist the force transmitted by beam
due to eccentric load flange
M,, moment resistance of tension P,, elastic buckling strength under
flange axial compression
Mu second order elastic moment;
Pcrip crippling strength of web of I-sec-
factored moment; required ultimate tion
flexural strength of a section Pd design axial compressive strength
My factored applied moment about the Pdy, Pdz design compression strength
minor axis of the cross section; yield mo-
as governed by flexural buckling about
ment capacity about minor axis
the respective axis
Myq yield moment capacity of the stiff-
Pdw design strength of fillet weld
ener about an axis parallel to web
P,, P,, elastic Euler buckling load;
M, factored applied moment about the *EI/L2
major axis of the cross section
Pf probability of failure
m mass; slope of the fatigue strength
Pk modal participation factor for mode
curve
k
m, mass of vth combustible material Pmin minimum required strength for
m1 non-dimensional moment param-
each flange splice
eter = MJMbp
PN probability that an event will be
Nd design strength in tension or in exceeded at least once in N years
compression
P, nominal axial strength
Nf axial force in the flange axial strength of the member bent
Pny
N,, number of stress cycles
about its weak axis
n number of parallel planes of battens;
P, maximum load in the column
mean probable design life of structure
p pitch length between centres of holes
in years; reduced frequency; number of
parallel to the direction of the load; pitch
cycles to failure; factored applied axial
of thread in bolt, pressure
force; number of bolts in the bolt group/
pd design wind pressure
critical section; number of stress cycles;
p,, p,,p 2 staggered pitch length along
number of storeys
the direction of the load between lines
nl, n2 dispersion length
of the bolt holes (Fig. 5.21)
n, number of effective interfaces of-
p, wind pressure at height Z
fering frictional resistance to slip
Q prying force; nominal imposed load;
n, number of shear planes with the static moment of the cross section =A5
threads intercepting the shear plane in a
Q* design imposed load
bolted connection
Q, accidental load (action)
n, number of shear planes without Q, characteristic load (action)
threads intercepting the shear plane in a
Qd design load (action)
bolted connection Qf fire load
n’ number of rows of bolts
Qj load effect i; design lateral force at
floor i
List of Symbols xxi
Q, mean value of load S, spectral displacement
Qp permanent loads (action) Sp spring stiffness
Q,, variable loads (action) S,, spectral velocity
qf fire loadhnit floor area S,, S, stability functions
R ratio of the mean compressive stress s design snow load; size of weld
in the web (equal to stress at mid depth) s, actual stiffener spacing
to yield stress of the web; reaction of
s, anchorage length of tension field
the beam at support; stress ratio; re- along the compression flange
sponse reduction factor; resultant force; sii,s jj stability functions
root opening of weld; local radius of
s* s.* stability function for semi-rigid
curvature of beam; return period 11' JJ
frames
R, design strength of the member at so ground snow load
room temperature
st anchorage length of tension field
R, net shear in bolt group at bolt i along the tension flange (distance be-
Rk connection stiffness
tween adjacent plastic hinges)
R, mean value of resistance
T Temperature in "C;f actored tension
R, nominal strength of resistance
in bolt; natural period of vibration; ap-
R,,, design strength of fillet weld per
plied torque
unit length
T, approximate fundamental natural
R,,, resultant force in the weld
period of vibration
R,. response reduction factor
Tb applied tension in bolt
Rtf resultant longitudinal shear in
T, design strength under axial tension
flange
Tdb design strength of bolt under axial
R, ultimate strength of the member at
tension; block shear strength of plate/
room temperature; ultimate strength of
angle
joint panel
P appropriate radius of gyration Tdg yielding strength of gross section
under axial tension
r, root radius of angle
Tdn rupture strength of net section un-
Pb root radius of beam flange
der axial tension; design tension capac-
r1 minimum radius of gyration of the
individual element being laced together ity
Tdw design strength of weld in tension
rf ratio of the design action on the
T, externally applied tension
member under fire to the design capac-
Teq equivalent fire rating time
ity
rVv radius of gyration about the minor Tf factored tension force of friction
type bolt; furnace temperature
axis (v-v)
T,,,, maximum temperature reached
r,, radius of gyration about the minor
in natural fire
axis
Tl limiting temperature of the steel
r, radius of gyration about the major
axis Tnb nominal strength of bolt under
axial tension
S minimum transverse distance be-
Tnd design tension capacity
tween the centroid of the rivet or bolt or
weld group; strouhal number; size re- Tndf design tensile strength of friction
type bolt
duction factor; spacing of truss
S, spectral acceleration T,, nominal tensile strength of friction
type bolt
xxii Design of Steel Structures
To ambient (room) temperature V,bf bearing capacity of bolt for fric-
T, steel temperature at time t tion type connection
Tt ambient gas temperature at time t Vp plastic shear resistance under pure
T, ultimate net section strength shear or shear strength of web
t thickness of elementhgle, time in V, nominal shear strength or resistance
minutes VnPb nominal bearing strength of bolt
t, thickness of top angle Vnsb nominal shear capacity of a bolt
tb thickness of base plate Vnsf nominal shear capacity of a bolt
tcw thickness of column web as governed by slip or friction type con-
te effective throat thickness of weld nection
thickness of flange; required fire rat- V,, factored shear force in the bolt
i)
ing time V,d design shear capacity
tfc thickness of compression flange V,df design shear strength of friction
tfail time to failure of the element in type bolt
case of fire V., factored design shear force of fric-
tfi thickness of beam flange tion bolts
tp thickness of plate/end plate V, applied transverse shear
tpkg thickness of packing V,, shear resistance in tension field
tq thickness of stiffeners V average or mean velocity
t, thickness of web stiffener; duration Vyw yield strength of web plate of I-
of fire section
t, time delay in minutes V, mean or design wind speed at
t, thickness of web height z above the ground
U shear lag factor V’ Instantaneous velocity fluctuation
V factored applied shear force; mean above the mean velocity
wind speed W appropriate load; width; seismic
V, total design seismic base shear; weight; ventilation factor
basic wind speed We equivalent cross-wind static force
Vb shear in batten plate per unit-height
Vbf factored frictional shear force in w uniform pressure from below on the
HSFG connection slab base due to axial compression un-
V,, critical shear strength correspond- der factored load; intensity of uniformly
ing to web buckling (without tension distributed load
field action) wtf width of tension field
V, design shear strength; design mean X distance from a point to any other
wind velocity point
Vdb shear capacity of outstanding leg xt torsional index
-
of cleat x distance from centre of gravity in x
Vdw design strength of weld in shear direction
Vg gradient wind speed; gust speed Y, yield stress
-
V, design wind speed at height h y distance from centre of gravity in y
V, longitudinal shear force direction
V, vector resultant shear in weld distance between point of applica-
yg
Vnb nominal shear strength of bolt tion of the load and shear centre of the
cross section