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


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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]

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 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.

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