Uniformly Distributed Load

Problem 611
Compute the value of EI δ at midspan for the beam loaded as shown in Fig. P-611. If E = 10 GPa, what value of I is required to limit the midspan deflection to 1/360 of the span?
 

Problem 610
The simply supported beam shown in Fig. P-610 carries a uniform load of intensity w_o symmetrically distributed over part of its length. Determine the maximum deflection δ and check your result by letting a = 0 and comparing with the answer to Problem 606.
 

Problem 590
A box beam carries a distributed load of 200 lb/ft and a concentrated load P as shown in Fig. P-590. Determine the maximum value of P if f_b ≤ 1200 psi and f_v ≤ 150 psi.
 

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 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 558

In Prob. 557, find the values of x and w_o so that w_o is a maximum.
 

Problem 557
A cast-iron beam 10 m long and supported as shown in Fig. P-557 carries a uniformly distributed load of intensity w_o (including its own weight). The allowable stresses are f_bt ≤ 20 MPa and f_bc ≤ 80 MPa. Determine the maximum safe value of w_o if x = 1.0 m.
 

Problem 555
A beam carries a concentrated load W and a total uniformly distributed load of 4W as shown in Fig. P-555. What safe value of W can be applied if f_bc ≤ 100 MPa and f_bt ≤ 60 MPa? Can a greater load be applied if the section is inverted? Explain.