Page 67 - Handbook of Civil Engineering Calculations, Second Edition

1.50 STRUCTURAL STEEL ENGINEERING AND DESIGN

Calculation Procedure:

1. Compute the maximum stress in the plate
If the maximum deflection of the plate is less than about one-half the thickness, the ef-
fects of diaphragm behavior may be disregarded.
2
Compute the maximum stress, using the relation f ( /8)(3 v)w(R/t) , where R
3
plate radius, in. (mm); t plate thickness, in. (mm); v Poisson’s ratio. Thus, f
2
( /8)(3.25)(20)(12/0.5) 14,000 lb/sq.in. (96,530.0 kPa).
3
2. Compute the maximum deflection of the plate
2
Use the relation y (1 v)(5 v)fR /[2(3 v)Et]
6
2
0.75(5.25)(14,000)(12) /[2(3.25)(30 10 )(0.5)] 0.081 in. (2.0574 mm). Since the de-
flection is less than one-half the thickness, the foregoing equations are valid in this case.
BENDING OF A RECTANGULAR FLAT PLATE
A 2 3 ft (61.0 91.4 cm) rectangular plate, simply supported along its periphery, is to
carry a uniform load of 8 lb/sq.in. (55.2 kPa) distributed over the entire area. If the allow-
able bending stress is 15,000 lb/sq.in. (103.4 MPa), what thickness of plate is required?

Calculation Procedure:

1. Select an equation for the stress in the plate
2 2
2
2 2
Use the approximation f a b w/[2(a b )t ], where a and b denote the length of the
plate sides, in. (mm).
2. Compute the required plate thickness
2
2 2
2
2
2
2
Solve the equation in step 1 for t. Thus t a b w/[2(a b )f ] 2 (3) (144)(8)/[2(2 2
2
3 )(15,000)] 0.106; t 0.33 in. (8.382 mm).
COMBINED BENDING AND AXIAL
LOAD ANALYSIS
A post having the cross section shown in Fig. 32 carries a concentrated load of 100 kips
(444.8 kN) applied at R. Determine the stress induced at each corner.
Calculation Procedure:

1. Replace the eccentric load with an equivalent system
Use a concentric load of 100 kips (444.8 kN) and two couples producing the following
moments with respect to the coordinate axes:

M x 100,000(2) 200,000 lb·in. (25,960 N·m)
M y 100,000(1) 100,000 lb·in. (12,980 N·m)