flexural 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.
 

To determine the load capacity or the size of beam section, it must satisfy the allowable stresses in both flexure (bending) and shear. Shearing stress usually governs in the design of short beams that are heavily loaded, while flexure is usually the governing stress for long beams. In material comparison, timber is low in shear strength than that of steel.
 

Problem 561
A T section has the dimensions given in Fig. P-561. Show that the neutral axis is 3 inches below the top and that I_NA = 166.7 in4. If the tensile stress at the bottom of the flange is 1000 psi, calculate (a) the total tensile force in the flange and (b) the total compressive force in the cross section. Also compute (c) the moment of the compressive force about the NA, and (d) the moment of the total tensile force about the NA. (e) How does the sum of (c) and (d) compare with the total applied bending moment as computed from the flexure formula?
 

Problem 559
A beam is composed of 6 planks, each 100 mm wide and 20 mm thick, piled loosely on each other to an overall dimension of 100 mm wide by 120 mm high. (a) Compare the strength of such a beam with that of a solid beam of equal overall dimensions. (b) What would be the ratio if the built-up beam consisted of a 12 planks each 100 mm wide by 10 mm thick?
 

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 556
A T beam supports the three concentrated loads shown in Fig. P-556. Prove that the NA is 3.5 in. above the bottom and that I_NA = 97.0 in⁴. Then use these values to determine the maximum value of P so that f_bt ≤ 4 ksi and f_bc ≤ 10 ksi.
 

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.