 
Section 8.7
Bending Member Summary
Beam strength is limited by flexural yielding, lateral torsional buckling,
flange local buckling, shear, and deflection. Local details of connections
are subject to the limit states of web local yielding and web crippling.
Limit States:
Limit State 
SCM Section 
f; W 
Equation(s) 
Strong Axis 
Flexure 
Chapter F 
0.9; 1.67 
Req'd M_{nx} = M_{ux}/f
or WM_{ax} < M_{nx} 
Y: 
F2.1 
 
M_{nx} = M_{px} = F_{y}Z_{x} 
LTB: 
F2.2, F3.1,
F4.2, F5.2 
 
 If L_{b} < L_{p}, M_{nx} = M_{px}
 If L_{p} < L_{b} < L_{r}, M_{nx}= [M_{px}(M_{px}M_{r})(L_{b}L_{p})/(L_{r}L_{p})]C_{b}
< M_{px}
 If L_{r} < L_{b}, M_{nx} = min[F_{cr}S_{x}, M_{px}]

FLB: 
F3.2, F4.3,
F5.3, F7.2,
F9.3 
 
 If l_{b} <
l_{p}, M_{nx} = M_{px}
 If l_{p} <
l_{b} <
l_{r}, M_{nx}= [M_{px}(M_{px}M_{r})(l_{b}l_{p})/(l_{r}l_{p})]
< M_{px}
 If l_{r} <
l_{b}, M_{nx} = min[F_{cr}S_{x}, M_{px}]

Shear 
Chapter G 
0.9; 1.67 
Req'd V_{nx} = V_{ux}/f
or WV_{ax} < V_{nx} 
Nominal Strength 
G2, G4, G5 
 
V_{nx} = M_{px} = 0.6F_{y}A_{w}C_{v
}Where C_{v} equation depends of web slenderness, h/t_{w} 
Deflection 
None 
N/A 
D_{LLx} <
D_{LLx,Allow} and
D_{TLx} < D_{TLx,Allow}
Other criteria as the project requires. 
Weak Axis 
Flexure 
Chapter F 
0.9; 1.67 
Req'd M_{ny} = M_{uy}/f
or WM_{ay} < M_{ny} 
Y: 
F6.1, F7.1,
F8.1 
 
M_{ny} = M_{py} = min[F_{y}Z_{y},
1.6F_{y}S_{y}] 
FLB: 
F6.2, F7.2 
 
 If l_{b} <
l_{p}, M_{ny} = M_{py}
 If l_{p} <
l_{b} <
l_{r}, M_{ny}= [M_{py}(M_{py}M_{r})(l_{b}l_{p})/(l_{r}l_{p})]
< M_{py}
 If l_{r} <
l_{b}, M_{ny} = F_{cr}S_{y}
< M_{py}

Shear 
Chapter G 
0.9; 1.67 
Req'd V_{n}_{y} = V_{uy}/f
or WV_{ay} < V_{ny} 
Nominal Strength 
G7 
 
V_{nx} = M_{px} = 0.6F_{y}A_{v}C_{v
}Where A_{v} = S(b_{f}t_{f}) 
Deflection 
None 
N/A 
D_{LLy} <
D_{LLy,Allow} and
D_{TLy} < D_{TLy,Allow}
Other criteria as the project requires. 
Local Considerations 
Web Local Yielding 
J10.2 
1.0; 1.50 
Req'd R_{n} = R_{u}/f
or WR_{a} < R_{n} 
Ends: 
J10.2 
 
R_{n} = SCM eq. J102 
Mid: 
J10.2 
 
R_{n} = SCM eq. J103 
Web Crippling 
J10.3 
0.75; 2.00 
Req'd R_{n} = R_{u}/f
or WR_{a} < R_{n} 
Ends: 
J10.3 
 
R_{n} = SCM eq. J104 
Mid: 
J10.3 
 
R_{n} = SCM eq. J105 
Selecting Sections:
Find the best section that satisfies all the applicable general limit states:
 Req'd M_{nx} < M_{nx }and/or_{ }Req'd
M_{ny} < M_{ny}
 Req'd V_{nx} < V_{nx }and/or_{ }Req'd
V_{ny} < V_{ny}
 D_{LLx} <
D_{LLx,Allow}, D_{TLx}
< D_{TLx,Allow}, D_{LLy}
< D_{LLy,Allow} and/or
D_{TLy} < D_{TLy,Allow}
Search methods include: Use of sorted section property tables, the
hunt & peck method, and the brute force method.
Cover Plates
Cover plates increase the plastic section modulus, Z, of a section.
 If the cover plates are symmetrically applied:
Z_{total} = Z_{beam} + Z_{plates}
= Z_{beam} + bt(d+t)
 If the cover plates are not symmetrically applied:
 Locate centroidal axis of section with cover plate
 Locate the centroids of each half of the total section above
and below the centroidal axis.
 Compute Z_{total} = [A_{total} /2] [distance
between centroids of each half]
In addition, cover plates
 must be compact (SCM Table B4.1a case 7)
 need to extend beyond the point where they are no longer needed
and connected with fillet welds or slipcritical bolts sufficient to
develop force in plates.
 Need to be attached sufficient to transfer horizontal shear
forces induced by bending. The spacing of fasteners can be computed
by:
s < minimum [ 2 r_{n} / q ,
t sqrt( E / (3 F_{y})) ]
Bearing Plate: Beams support by concrete
The general procedure for designing a base plate is as follows:
 Select the plate width, N, based on the limits of available space, web
local yielding, and web crippling.
 Select the plate length, B, based on the limit state of bearing strength
of concrete. If N_{2} can be determined, then B can be
determined by:
B > Req'd P_{p} / (f'_{c} min[0.85 N_{2},
1.7 N_{1}])
 Select t based on the plate's flexural strength
Note that the values for f and
W vary with limit state so the values or req'd strength (Req'd R_{n}
= (R_{u}/f or R_{a}W)
and Req'd P_{p} = (R_{u}/f or R_{a}W))
will vary with f and W.
Final dimensions should be chosen that are easy to measure in whatever unit
system the design is being created in.
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