rectangular beam

Problem
A beam 100 mm wide is to be loaded with 3 kN concentrated loads spaced uniformly at 0.40 m on centers throughout the 5 m span. The following data are given:

1. Find the depth d considering bending stress only.
2. Determine the depth d considering shear stress only.
3. Calculate the depth d considering deflection only.

Problem
A timber beam 4 m long is simply supported at both ends. It carries a uniform load of 10 kN/m including its own weight. The wooden section has a width of 200 mm and a depth of 260 mm and is made up of 80% grade Apitong. Use dressed dimension by reducing its dimensions by 10 mm.

1. What is the maximum flexural stress of the beam?
2. What is the maximum shearing stress of the beam?
3. What is the maximum deflection of the beam?

Problem
A reinforced concrete beam 300 mm wide has an effective depth of 600 mm. It is reinforced with 4-32 mm diameter bars for tension. f’_c = 21 MPa and f_y = 275 MPa. Find the moment capacity of the beam.
 

Problem
A rectangular concrete beam is reinforced in tension only. The width is 300 mm and the effective depth is 600 mm. The beam carries a moment of 80 kN·m which causes a stress of 5 MPa in the extreme compression fiber of concrete. Use n = 9.
1.   What is the distance of the neutral axis from the top of the beam?
2.   Calculate the required area for steel reinforcement.
3.   Find the stress developed in the steel.
 

Problem 690
The beam shown in Fig. P-690 has a rectangular cross section 50 mm wide. Determine the proper depth d of the beam if the midspan deflection of the beam is not to exceed 20 mm and the flexural stress is limited to 10 MPa. Use E = 10 GPa.
 

Problem 642
Find the maximum deflection for the cantilever beam loaded as shown in Figure P-642 if the cross section is 50 mm wide by 150 mm high. Use E = 69 GPa.
 

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 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.