Handbook of Civil Engineering Calculations

Where Avg = gross area of the vertical part of (2)

Ans = net area of the vertical part of (2)

Ag = gross area of the horizontal part of (2)

An = net area of the horizontal part of (2)

Avg = (I^1 X 2 in^2 x 3 in) x 0.515 in = 3.86 in^2 (24.9 cm^2 )

Ans = (I^1 X 2 in + 2 x 3 in x 21 X 2 x «/ 16 ) x 0.515 in = 2.66 in^2 (17.2 cm^2 )

Ag = I^1 X 2 in x 0.515 in = 0.77 in^2 (4.96 cm^2 )

An = (I^1 X 2 in -^1 X 2 x^15 X 16 in) x 0.515 in = 0.53 in^2 (3.42 cm^2 )

2. Determine the design shear strength
   Rn is the greater of

0.6 x 3.86 in^2 x 36 -^- + 0.53 in^2 x 56 -^- = 114 kips (507 kN)

in^2 in^2

0.6 x 2.66 in^2 x 58 -^- + 0.77 in^2 x 36 ^- = 120 kips (533.8 kN)

in^2 in^2

Rn =120 kips (533.8 kN)

<t>Rn = 0.75 x 120 kips = 90 kips (400.3 kN)

The design shear strength is 90 kips (400.3 kN), based on the governing limit state of
block shear rupture.

Related Calculations. This procedure is the work of Abraham J. Rokach, MSCE,
Associate Director of Education, American Institute of Steel Construction. SI values were
prepared by the handbook editor.

DESIGNING A BEARING PLATE FOR A BEAM

AND ITS END REACTION

The unstiffened end of a W21 x 62 beam in A3 6 steel rests on a concrete support (/,' = 3

ksi) [20.7 MPa], Fig. 50. Design a bearing plate for the beam and its (factored) end reac-

tion of 100 kips (444.8 kN). Assume the area of concrete support A 2 = 6 x A 1 (the area of

the bearing plate).

Calculation Procedure:

1. Find the bearing length
   For the concentrated compressive reaction of 100 kips (444.8 kN) acting on the bottom
   flange, the applicable limit states are (1) local web yielding and (2) web crippling. (It is
   assumed that the beam is welded to the base plate and both are anchor-bolted to the con-
   crete support. This should provide adequate lateral bracing to prevent sidesway web
   buckling.)