Question 3.20: An alternative proposal for supporting the bar described in ...
An alternative proposal for supporting the bar described in Example Problem 3–19 is shown in Figure 3–17. To allow for expansion of the bar, the left end is supported on a 50.0 mm diameter roller made from SAE 1040 CD steel. Compute the allowable load, W, for this arrangement.
Objective Compute the allowable load on the beam.
Given Loading in Figure 3–17.
Width of the beam (t = 32.0 mm) rests on the roller (d = 50.0 mm).
Beam material: ASTM A36 structural steel (s_{y} = 248 MPa).
Roller material: SAE 1040 CD (s_{y} = 565 MPa).
Analysis At the roller support, Equation (3–24) applies to determine the allowable load. Note that W = 2R_{a} . Use s_{y} = 248 MPa, the weaker of the two materials in contact.
Results The allowable bearing load is
R_{a} = (S_{y} -90)(3.0 \times 10^{-5})(d)(L) (3-24)
This would be the allowable reaction at each support. The total load is
W = 2R_{a} = 2 (7.58 kN) = 15.17 kN
Comment Note that this is significantly lower than the allowable load for the surfaces found in Example Problem 3–19. Bearing at the roller support may, indeed, limit the load that could be safely supported.