Calculation Procedure:- 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.
Compute the maximum stress, using the relation/= (^3 Xs)(S + v)w(R/t)^2 , where R = plate
radius, in (mm); t = plate thickness, in (mm); v = Poisson's ratio. Thus, / =
(^3 /8)(3.25)(20)(12/0.5)^2 = 14,000 lb/in^2 (96,530.0 kPa). - Compute the maximum deflection of the plate
Use the relation^ = (1 - v)(5 + v)/R^2 /[2(3 + V)Et] = 0.75(5.25)(14,000)(12)^2 /[2(3.25)(30 x
106 )(0.5)] = 0.081 in (2.0574 mm). Since the deflection is less than one-half the thickness,
the foregoing equations are valid in this case.
BENDING OFA RECTANGULAR FLATPLATEA2 x 3 ft (61.Ox 91.4 cm) rectangular plate, simply supported along its periphery, is to
carry a uniform load of 8 lb/in^2 (55.2 kPa) distributed over the entire area. If the allowable
bending stress is 15,000 lb/in^2 (103.4 MPa), what thickness of plate is required?
Calculation Procedure:- Select an equation for the stress in the plate
Use the approximation/= a^2 b^2 w/[2(a^2 + b^2 )t^2 ], where a and b denote the length of the
plate sides, in (mm). - Compute the required plate thickness
Solve the equation in step 1 for t. Thus t
2
= a
2
b
2
w/[2(a
2
- b
2
)f] = 2
2
(3)
2
(144)(8)/[2(2
2
32 )(15,000)] = 0.106; t = 0.33 in (8.382 mm).
COMBINED BENDING AND AXIAL
LOAD ANALYSISA 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:
- 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:
Mx = 100,000(2) = 200,000 lb-in (25,960 N-m)My = 100,000(1) = 100,000 lb-in (12,980 N-m)