18 - 20 Rectangular beam in maxima and minima problems
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.
Solution to Problem 567 | Horizontal Shearing Stress
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
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.
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Solution to Problem 526 | Flexure Formula
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?
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Solution to Problem 522 | Flexure Formula
Problem 522
A box beam is composed of four planks, each 2 inches by 8 inches, securely spiked together to form the section shown in Fig. P-522. Show that INA = 981.3 in4. If wo = 300 lb/ft, find P to cause a maximum flexural stress of 1400 psi.
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Solution to Problem 517 | Flexure Formula
Problem 517
A rectangular steel bar, 15 mm wide by 30 mm high and 6 m long, is simply supported at its ends. If the density of steel is 7850 kg/m3, determine the maximum bending stress caused by the weight of the bar.
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Solution to Problem 511 | Flexure Formula
Problem 511
A simply supported rectangular beam, 2 in wide by 4 in deep, carries a uniformly distributed load of 80 lb/ft over its entire length. What is the maximum length of the beam if the flexural stress is limited to 3000 psi?
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