August 2009

Problem 589
A channel section carries a concentrated loads W and a total distributed load of 4W as shown in Fig. P-589. Verify that the NA is 2.17 in. above the bottom and that I_NA = 62 in⁴. Use these values to determine the maximum value of W that will not exceed allowable stresses in tension of 6,000 psi, in compression of 10,000 psi, or in shear of 8,000 psi.
 

Problem 588
The distributed load shown in Fig. P-588 is supported by a wide-flange section of the given dimensions. Determine the maximum value of w_o that will not exceed a flexural stress of 10 MPa or a shearing stress of 1.0 MPa.
 

Problem 587
A beam carries two concentrated loads P and triangular load of 3P as shown in Fig. P-587. The beam section is the same as that in Fig. P-577 on this page. Determine the safe value of P if f_b ≤ 1200 psi and f_v ≤ 200 psi.
 

Problem 586
The distributed load shown in Fig. P-586 is supported by a box beam having the same cross-section as that in Prob. 585. Determine the maximum value of w_o that will not exceed a flexural stress of 10 MPa or a shearing stress of 1.0 MPa.
 

Problem 585
A simply supported beam of length L carries a uniformly distributed load of 6000 N/m and has the cross section shown in Fig. P-585. Find L to cause a maximum flexural stress of 16 MPa. What maximum shearing stress is then developed?
 

Problem 584
A wide-flange section having the dimensions shown in Fig. P-584 supports a distributed load of w_o lb/ft on a simple span of length L ft. Determine the ratio of the maximum flexural stress to the maximum shear stress.
 

Problem 583
A rectangular beam 6 in. wide by 10 in. high supports a total distributed load of W and a concentrated load of 2W applied as shown in Fig. P-583. If f_b ≤ 1500 psi and f_v ≤ 120 psi, determine the maximum value of W.
 

Problem 582
Find the cross-sectional dimensions of the smallest square beam that can be loaded as shown in Fig. P-582 if f_v ≤ 1.0 MPa and f_b ≤ 8 MPa.
 

Problem 581
A laminated beam is composed of five planks, each 6 in. by 2 in., glued together to form a section 6 in. wide by 10 in. high. The allowable shear stress in the glue is 90 psi, the allowable shear stress in the wood is 120 psi, and the allowable flexural stress in the wood is 1200 psi. Determine the maximum uniformly distributed load that can be carried by the beam on a 6-ft simple span.
 

Problem 580
A rectangular beam of width b and height h carries a central concentrated load P on a simply supported span of length L. Express the maximum f_v in terms of maximum f_b.