Beam Summary

A Beginner's Guide to the Steel Construction Manual, 13^th ed. (old)

Chapter 8 - Bending Members

Introduction

Flexure

Shear

Deflection

Misc. Limit States

Beam Design

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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 M_nx = M_ux/f or WM_ax < M_nx
Y:	F2.1	------	M_nx = M_px = F_yZ_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_crS_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_crS_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_yA_wC_vWhere 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_yZ_y, 1.6F_yS_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_crS_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_yA_vC_vWhere A_v = S(b_ft_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. J10-2
Mid:	J10.2	------	R_n = SCM eq. J10-3
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. J10-4
Mid:	J10.3	------	R_n = SCM eq. J10-5

Selecting Sections:

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

Req'd M_nx < M_nxand/orReq'd M_ny < M_ny
Req'd V_nx < V_nxand/orReq'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 B4.1 case 12)
need to extend beyond the point where they are no longer needed.
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 N₂ can be determined, then B can be determined by:
B > Req'd P_p / (f'_c min[0.85 N₂, 1.7 N₁])
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_aW) and Req'd P_p = (R_u/f or R_aW)) 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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