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.
 

Let us consider a differential length dx of the beam shown
 

For the upper shaded portion of the beam, the forces acting are the total normal forces F_R and F_L due to the bending stresses to the left and to the right of the beam. These forces will be resisted by the shearing force f_vb dx acting at the boundary surface between the shaded and the unshaded portions.
 

If a beam is composed of two or more thin layers placed on each other without any attachment, the separate layers would slide past each other and the total strength of the beam would be the sum of the strengths of the various layers. The strength of this beam is lesser than a solid beam having the same cross-sectional area.
 

Problem 553
Determine the maximum tensile and compressive bending stresses developed in the beam as shown in Fig. P-553.
 

Problem 552
A cantilever beam carries the force and couple shown in Fig. P-552. Determine the maximum tensile and compressive bending stresses developed in the beam.
 

Problem 551
Find the maximum tensile and compressive flexure stresses for the cantilever beam shown in Fig. P-551.
 

Problem 550
Resolve Prob. 549 if the maximum moments are +2.5P lb·ft and -5.0P lb·ft.
 

Problem 549
A beam with cross-section shown in Fig. P-549 is loaded in such a way that the maximum moments are +1.0P lb·ft and -1.5P lb·ft, where P is the applied load in pounds. Determine the maximum safe value of P if the working stresses are 4 ksi in tension and 10 ksi in compression.
 

Problem 548
The inverted T section of a 4-m simply supported beam has the properties shown in Fig. P-548. The beam carries a uniformly distributed load of intensity w_o over its entire length. Determine w_o if f_bt ≤ 40 MPa and f_bc ≤ 80 MPa.
 

Problem 543
A portion of the floor plan of a building is shown in Fig. P-543. The total loading (including live and dead loads) in each bay is as shown. Select the lightest suitable W-shape if the allowable flexural stress is 120 MPa.