Unsymmetrical Beam

Problem 595
A concentrated load P is carried at midspan of a simply supported 12-ft span. The beam is made of 2-in. by 6-in. pieces screwed together, as shown in Fig. P-595. If the maximum flexural stress developed is 1400 psi, find the maximum shearing stress and the pitch of the screws if each screw can resist 200 lb.
 

Problem 564
Repeat Prob. 563 using 2-in. by 10-in. pieces.
 

Problem 563
A box beam is made from 2-in. by 6-in. pieces screwed together as shown in Fig. P-563. If the maximum flexure stress is 1200 psi, compute the force acting on the shaded portion and the moment of this force about the NA. Hint: Use the results of Prob. 562.
 

Problem 562
In any beam section having a maximum stress f_b, show that the force on any partial area A' in Fig. P-562 is given by F = (f_b/c)A'(barred y') , where (barred y') is the centroidal coordinate of A'. Also show that the moment of this force about the NA is M' = f_b I'/c, where I' is the moment of inertia of the shaded area about the NA.
 

Problem 558

In Prob. 557, find the values of x and w_o so that w_o is a maximum.
 

Problem 557
A cast-iron beam 10 m long and supported as shown in Fig. P-557 carries a uniformly distributed load of intensity w_o (including its own weight). The allowable stresses are f_bt ≤ 20 MPa and f_bc ≤ 80 MPa. Determine the maximum safe value of w_o if x = 1.0 m.
 

Problem 556
A T beam supports the three concentrated loads shown in Fig. P-556. Prove that the NA is 3.5 in. above the bottom and that I_NA = 97.0 in⁴. Then use these values to determine the maximum value of P so that f_bt ≤ 4 ksi and f_bc ≤ 10 ksi.
 

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

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.
 

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