A Beginner's Guide to the Steel Construction Manual, 14th ed. Chapter 8 - Bending Members © 2006, 2007, 2008, 2011 T. Bartlett Quimby
 Introduction Flexure Shear Deflection Misc. Limit States Beam Design Chapter Summary Example Problems Homework Problems References Report Errors or Make Suggestions Purchase Hard Copy

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 Mnx = Mux/f or WMax < Mnx Y: F2.1 ------ Mnx = Mpx = FyZx LTB: F2.2, F3.1, F4.2, F5.2 ------ If Lb < Lp, Mnx = Mpx If Lp < Lb < Lr, Mnx= [Mpx-(Mpx-Mr)(Lb-Lp)/(Lr-Lp)]Cb < Mpx If Lr < Lb, Mnx = min[FcrSx, Mpx] FLB: F3.2, F4.3, F5.3, F7.2, F9.3 ------ If lb < lp, Mnx = Mpx If lp < lb < lr, Mnx= [Mpx-(Mpx-Mr)(lb-lp)/(lr-lp)] < Mpx If lr < lb, Mnx = min[FcrSx, Mpx] Shear Chapter G 0.9; 1.67 Req'd Vnx = Vux/f or WVax < Vnx Nominal Strength G2, G4, G5 ------ Vnx = Mpx = 0.6FyAwCv Where Cv equation depends of web slenderness, h/tw Deflection None N/A DLLx < DLLx,Allow and DTLx < DTLx,Allow Other criteria as the project requires. Weak Axis Flexure Chapter F 0.9; 1.67 Req'd Mny = Muy/f or WMay < Mny Y: F6.1, F7.1, F8.1 ------ Mny = Mpy = min[FyZy, 1.6FySy] FLB: F6.2, F7.2 ------ If lb < lp, Mny = Mpy If lp < lb < lr, Mny= [Mpy-(Mpy-Mr)(lb-lp)/(lr-lp)] < Mpy If lr < lb, Mny = FcrSy < Mpy Shear Chapter G 0.9; 1.67 Req'd Vny = Vuy/f or WVay < Vny Nominal Strength G7 ------ Vnx = Mpx = 0.6FyAvCv Where Av = S(bftf) Deflection None N/A DLLy < DLLy,Allow and DTLy < DTLy,Allow Other criteria as the project requires. Local Considerations Web Local Yielding J10.2 1.0; 1.50 Req'd Rn = Ru/f or WRa < Rn Ends: J10.2 ------ Rn = SCM eq. J10-2 Mid: J10.2 ------ Rn = SCM eq. J10-3 Web Crippling J10.3 0.75; 2.00 Req'd Rn = Ru/f or WRa < Rn Ends: J10.3 ------ Rn = SCM eq. J10-4 Mid: J10.3 ------ Rn = SCM eq. J10-5

Selecting Sections:

Find the best section that satisfies all the applicable general limit states:

• Req'd Mnx < Mnx and/or Req'd Mny < Mny
• Req'd Vnx < Vnx and/or Req'd Vny < Vny
• DLLx < DLLx,Allow, DTLx < DTLx,Allow, DLLy < DLLy,Allow and/or DTLy < DTLy,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:

Ztotal = Zbeam + Zplates = Zbeam + 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 Ztotal = [Atotal /2] [distance between centroids of each half]

• 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 slip-critical 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 rn / q , t sqrt( E / (3 Fy)) ]

Bearing Plate:  Beams support by concrete

The general procedure for designing a base plate is as follows:

1. Select the plate width, N, based on the limits of available space, web local yielding, and web crippling.
2. Select the plate length, B, based on the limit state of bearing strength of concrete.  If N2 can be determined, then B can be determined by:

B > Req'd Pp / (f'c min[0.85 N2, 1.7 N1])

3. 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 Rn = (Ru/f or RaW) and Req'd Pp = (Ru/f or RaW)) 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.