18 - 20 Rectangular beam in maxima and minima problems Jhun Vert Mon, 05/04/2020 - 10:23 pm

Problem 18
The strength of a rectangular beam is proportional to the breadth and the square of the depth. Find the shape of the largest beam that can be cut from a log of given size.
 

Problem 19
The stiffness of a rectangular beam is proportional to the breadth and the cube of the depth. Find the shape of the stiffest beam that can be cut from a log of given size.
 

Problem 20
Compare for strength and stiffness both edgewise and sidewise thrust, two beams of equal length, 2 inches by 8 inches and the other 4 inches by 6 inches (See Problem 18 and Problem 19 above). Which shape is more often used for floor joist? Why?
 

Solution to Problem 642 | Deflection of Cantilever Beams Jhun Vert Thu, 04/23/2020 - 08:30 pm

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.
 

Uniform load over the free end of cantilever beam

 

Solution to Problem 570 | Horizontal Shearing Stress Jhun Vert Wed, 04/22/2020 - 11:04 pm

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.
 

Rectangular box beam

 

Solution to Problem 567 | Horizontal Shearing Stress Jhun Vert Wed, 04/22/2020 - 10:40 pm

Problem 567
A timber beam 80 mm wide by 160 mm high is subjected to a vertical shear V = 40 kN. Determine the shearing stress developed at layers 20 mm apart from the top to bottom of the section.
 

Solution to Problem 527 | Flexure Formula Jhun Vert Wed, 04/22/2020 - 10:59 am

Problem 527
In Prob. 526, if the load on the overhang is 600 lb/ft and the overhang is x ft long, find the maximum values of P and x that can be used simultaneously.
 

Rectangular wood beam

 

Solution to Problem 526 | Flexure Formula Jhun Vert Wed, 04/22/2020 - 10:51 am

Problem 526
A wood beam 6 in wide by 12 in deep is loaded as shown in Fig. P-526. If the maximum flexural stress is 1200 psi, find the maximum values of wo and P which can be applied simultaneously?
 

Rectangular wood beam