Nomenclature
A area in2
A1 loaded area in2
A2 maximum area of supporting surface that is geometrically similar to and concentric with loaded area A1
in2
b width in
B width of plate in
d depth in
D dead load lbf
E modulus of elasticity lbf/in2
fc′ specified compressive strength of concrete lbf/in2
F strength or stress lbf/in2
h height in
I moment of inertia in4
k distance from outer face of flange to web toe of fillet
in kc coefficient for slender unstiffened elements – kdes distance from outer face of flange to web toe of
fillet, as a decimal value for design calculations in kdet distance from outer face of flange to web toe of
fillet, as a fractional value for detailing calculations
in
K effective length factor –
KL effective length in
KL/r slenderness ratio –
lb length of bearing in
L length in
L live load lbf
M moment, flexural strength, or moment strength in-lbf
n effective cantilever length in
6
p bearing stress lbf/in2
P axial strength lbf
P force lbf
r radius of gyration in
R strength lbf
R1, R3, R5 beam end bearing constants lbf R2, R4, R6 beam end bearing constants lbf/in
S elastic section modulus in3
t thickness in
w load per unit length lbf/in
x distance from end of member in
Z plastic section modulus in3
Symbols
φ resistance factor (LRFD) –
Ω safety factor (ASD) –
Subscripts
a required (ASD)
c compression flange cr critical
cross cross-shaped column e elastic critical buckling (Euler) eff effective
f flange
g gross
max maximum min minimum n net or nominal p plastic bending req required st stiffener
u required (LRFD) or ultimate tensile
w web
x about x-axis
y about y-axis or yield
1. INTRODUCTION
The design requirements for concentrated loads applied to flanges and webs of I-shaped members are contained in Sec. J10 of the AISC Specification, which governs design considerations for the following limit states.
• flange local bending (AISC Sec. J10.1)
• web local yielding (AISC Sec. J10.2)
• web local crippling (AISC Sec. J10.3)
• web sidesway buckling (AISC Sec. J10.4)
• web compression buckling (AISC Sec. J10.5)
• web panel zone shear (AISC Sec. J10.6)
The required strength must be less than or equal to the available strength.
[
LRFD]
u n
R
≤ φ
R 6.1[
ASD]
n a
R ≤ R
Ω 6.2
When the required strength is greater than the available strength for the applicable limit states, transverse stiffener plates (also called continuity plates) or doubler plates and their attaching welds must be sized for the difference between required and available strengths. Figure 6.1 shows the use of stiffener plates and doubler plates.
Figure 6.1 Stiffener Plates and Doubler Plates
stiffener plates: perpendicular to web of beam or column
doubler plates: parallel to web of beam or column
In Fig. 6.2, forces P1 and P2 induce single tensile forces on the flange and web. Forces P3 and P4 induce single compressive forces on the flange and web. Moments M1 and M2 double the tensile forces P5 and P7 and double the compressive forces P6 and P8 on the flanges and web of the beam.
Figure 6.2 I-Shaped Beam with Flanges and Webs Subjected to Concentrated Loads
Forces P1 and P4 are applied at a distance from the end of the beam that is less than or equal to the beam depth, d. Forces P2 and P3 are applied at a distance from the beam end greater than d. This distinction often affects calculations, as shown later in this chapter.
2. FLANGE LOCAL BENDING
The limit state of flange local bending applies to tensile single-concentrated forces and the tensile component of double-concentrated forces.
For the limit state of flange local bending, the design strength, φRn, and the allowable strength, Rn /Ω, are calculated using Eq. 6.3 for the value of Rn. For LRFD, φ = 0.90, and for ASD, Ω = 1.67.
[ ]
2 AISC Eq. J10-1
n
6.25
yf fR
=
F t 6.3If the length of the loading across the member flange is less than 0.15 times the flange width, 0.15bf, Eq. 6.3 need not be checked.
When the concentrated force to be resisted is applied at a distance less than 10tf from the end of the member, then Rn must be reduced by 50%. When required, use a pair of transverse stiffeners.
d
N N
P2 P1
d d
P4 P3
P7 M2 P8
P5 P6
M1
3. WEB LOCAL YIELDING
This section applies to single-concentrated forces and both components of double-concentrated forces. Figure 6.3 shows the nomenclature used in calculating web yielding and web crippling.
Figure 6.3 Nomenclature for Web Yielding and Web Crippling
For the limit state of web local yielding, φ = 1.00 (LRFD) and Ω = 1.50 (ASD).
Available strength is determined as follows.
When the concentrated force to be resisted is applied at a distance greater than d from the end of the member, the nominal strength is
( 5 ) [
AISC Eq. J10-2]
n yw w b
R
=
F t k l+
6.4When the concentrated force to be resisted is applied at a distance of d or less from the end of the member, the nominal strength is
( 2.5 ) [
AISC Eq. J10-3]
n yw w b
R
=
F t k l+
6.5In these equations, k is the distance from the outer face of the flange to the web toe of the fillet, and lb is the length of bearing (not less than k for end beam reactions). For W-series beams, use kdes and not kdet from AISC Manual Table 1-1, because these are engineering calculations and not detailing dimensions. When required, a pair of transverse web stiffeners or a doubler plate must be provided.
4. WEB LOCAL CRIPPLING
This section applies to compressive single-concentrated forces or the compressive component of double-concentrated forces. For the limit state of web crippling, φ = 0.75 (LRFD) and Ω = 2.00 (ASD). The available strength is determined as follows.
When the concentrated compressive force to be resisted is applied at a distance of d/2 or more from the end of the member, then the nominal strength is
[ ]
1.5
2 AISC Eq. J10-4
0.80 1 3
b w yw fn w
f w
l t EF t
R t
d t t
= +
6.6
toe of fillet
lb + 2.5k
tw lb + 5k
k
d k
lb
lb
When the concentrated compressive force to be resisted is applied at a distance less than d/2 from the end of the member, then the nominal strength is calculated with Eq. 6.7 or Eq. 6.8, depending on the value of lb/d.