Question 3.19: A short beam, shown in Figure 3–16, is made from a rectangul...
A short beam, shown in Figure 3–16, is made from a rectangular steel bar, 32.0 mm thick and120 mm high. At each end, the length resting on a steel plate is 50.0 mm. If both the bar and the plate are made from ASTM A36 structural steel, compute the maximum allowable load, W, which could be carried by the beam, based on only the bearing stress at the supports. The load is centered between the supports.
Objective Compute the allowable load, W, based on only bearing stress.
Given Loading in Figure 3–16.
Bearing area at each end: t = 32.0 mm × a = 50.0 mm (that is, A_{b} = ta).
Material: ASTM A36 structural steel ( s_{y} = 248 MPa).
Analysis Design bearing stress \sigma_{bd} = R_{a}/A_{b}
Where R_{a} is the allowable reaction at the support and R_{a} = W/2.
Design stress Equation (3–22):
\sigma_{bd} = 0.90 s_{y} = 0.90(248 \times 10^{6} N/m² ) = 223 MPa
Then, R_{a} = A_{b} \sigma_{bd} and W = 2R_{a} .
Results Bearing area: A_{b} = ta = (32.0 mm)(50.0 mm) = 1600 mm².
R_{a} = A_{b} \sigma_{bd} = (1600 mm²) (223 N/mm²) = 356 800 N
W = 2R_{a} = 2(356 800 N) = 713 600 N = 713.6 kN
Comment This is a very large load, so it is unlikely that bearing is the mode of failure for this beam.