Moment Diagram by Parts

The moment-area method of finding the deflection of a beam will demand the accurate computation of the area of a moment diagram, as well as the moment of such area about any axis. To pave its way, this section will deal on how to draw moment diagram by parts and to calculate the moment of such diagrams about a specified axis.
 

Solution to Problem 589 | Design for Flexure and Shear

Problem 589
A channel section carries a concentrated loads W and a total distributed load of 4W as shown in Fig. P-589. Verify that the NA is 2.17 in. above the bottom and that INA = 62 in4. Use these values to determine the maximum value of W that will not exceed allowable stresses in tension of 6,000 psi, in compression of 10,000 psi, or in shear of 8,000 psi.
 

Solution to Problem 555 | Unsymmetrical Beams

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 fbc ≤ 100 MPa and fbt ≤ 60 MPa? Can a greater load be applied if the section is inverted? Explain.
 

Solution to Problem 554 | Unsymmetrical Beams

Problem 554
Determine the maximum tensile and compressive stresses developed in the overhanging beam shown in Fig. P-554. The cross-section is an inverted T with the given properties.
 

Solution to Problem 531 | Economic Sections

Problem 531
A 15-ft beam simply supported at the ends carries a concentrated load of 9000 lb at midspan. Select the lightest S section that can be employed using an allowable stress of 18 ksi. What is the actual maximum stress in the beam selected?