Symmetrical Load

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.