CIVIL ENGINEERING FORMULAS

218 CHAPTER NINE

To minimize material requirements, the plate projections should be nearly
equal. For this purpose, the plate length N, in (mm) (in the direction of d), may
be taken as

(9.39)

The width B, in (mm), of the plate then may be calculated by dividing A 1 byN.
BothBandNmay be selected in full inches (millimeters) so that BNA 1. In
that case, the bearing pressure fp, ksi (MPa), may be determined from the preced-
ing equation. Thickness of plate, determined by cantilever bending, is given by

(9.40)

whereFyminimum specified yield strength, ksi (MPa), of plate; and p
larger of 0.5(N0.95d) and 0.5(B0.80b).
When the plate projections are small, the area A 2 should be taken as the maxi-
mum area of the portion of the supporting surface that is geometrically similar to
and concentric with the loaded area. Thus, for an H-shaped column, the column
load may be assumed distributed to the concrete over an H-shaped area with flange
thicknessL, in (mm), and web thickness 2L:

(9.41)

whereFpallowable bearing pressure, ksi (MPa), on support. (If Lis an imaginary
number, the loaded portion of the supporting surface may be assumed rectangular
as discussed earlier.) Thickness of the base plate should be taken as the larger of the
values calculated from the preceding equation and

(9.42)

BEARING ON MILLED SURFACES

In building construction, allowable bearing stress for milled surfaces, including
bearing stiffeners, and pins in reamed, drilled, or bored holes, is Fp0.90Fy,
whereFyis the yield strength of the steel, ksi (MPa).
For expansion rollers and rockers, the allowable bearing stress, kip/linear in
(kN/mm), is

(9.43)

wheredis the diameter, in (mm), of the roller or rocker. When parts in contact
have different yield strengths, Fyis the smaller value.

Fp

Fy 13

20

0.66d

tL

B

3 fp

Fb

L

1

4

(db)

1

4 B

(db)^2 

4 R

Fp

t 2 p

B

fp

Fy

NA 1 0.5(0.95d0.80b)