box beam

Problem
A beam is built up by nailing together 25 mm thick planks to form a 200 mm × 250 mm box section as shown. The nails are spaced 125 mm apart and each can carry a shearing force of up to 1.3 kN. The beam is simply supported for a span of 3.6 m and to carry a concentrated load P at the third point of the span. The allowable shearing stress of the section is 0.827 MPa.
 

1. Determine the largest value of P that will not exceed the allowable shearing stress of the beam or the allowable shearing force of the nails.
2. What is the maximum flexural stress of the beam for the load P computed in Part (1)?

Problem
A concentrated load P is carried at midspan by a simply supported 4-m span beam. The beam is made of 40-mm by 150-mm timber screwed together, as shown. The maximum flexural stress developed is 8.3 MPa and each screw can resist 890 N of shear force.
 

1.   Determine the spacing of screws at A.
2.   Determine the spacing of screws at B.

Problem 595
A concentrated load P is carried at midspan of a simply supported 12-ft span. The beam is made of 2-in. by 6-in. pieces screwed together, as shown in Fig. P-595. If the maximum flexural stress developed is 1400 psi, find the maximum shearing stress and the pitch of the screws if each screw can resist 200 lb.
 

Problem 594
A distributed load of w_o lb/ft is applied over a middle 6 ft of a simply supported span 12 ft long. The beam section is that in Prob. 593, but used here so that the 8-in dimension is vertical. Determine the maximum value of w_o if f_b ≤ 1200 psi, f_v ≤ 120 psi, and the screws have a shear strength of 200 lb and a pitch of 2 in.
 

Problem 593
A box beam, built up as shown in Fig. P-593, is secured by screws spaced 5 in. apart. The beam supports a concentrated load P at the third point of a simply supported span 12 ft long. Determine the maximum value of P that will not exceed f_v = 120 psi in the beam or a shearing force of 300 lb in the screws. What is the maximum flexural stress in the beam?
 

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 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 571
For a beam with the same cross section as that in Prob. 570, plot the shearing stress distribution across the section at a section where the shearing force is V = 1800 lb.
 

Problem 570
A uniformly distributed load of 200 lb/ft is carried on a simply supported beam span. If the cross-section is as shown in Fig. P-570, determine the maximum length of the beam if the shearing stress is limited to 80 psi. Assume the load acts over the entire length of the beam.