Use the Euler buckling equation to determine the load P.. at which the column buckles. Indicate whether the column buckles around the x or y axis. Sketch the buckled shape, and locate and label the inflection points on the sketch. The support at the top of the column allows displacement in only the z direction and allows rotation about only the x-axis. The pin support at the bottom of the column does not allow displacement in any direction but allows rotation around all axes. Use L = 40 in, b=0.375 in, h=0.3 in, and E = 10,000 ksi. Po h b 1P Per L x

For the beam shown: (a) determine the distance a for which the maximum positive and negative bending moments in the beam are equal; and (b) draw the corresponding shear and bending moment diagrams for the beam.

A beam is part of the framing system for the floor of an office building. The floor is subjected to both dead loads and live loads. The maximum moment caused by the service dead load is 45 ft-kips, and the maximum moment for the service live load is 63 ft-kips (these moments occur at the same location on the beam and can therefore be combined). a. If load and resistance factor design is used, determine the maximum factored bending moment (required moment strength). What is the controlling AISC load combination? b. What is the required nominal moment strength for a resistance factor of 0.90? c. If allowable strength design is used, determine the required moment strength. What is the controlling AISC lead combination? d. What is the required nominal moment strength for a safety factor of 1.67?

Two line loads q1 and q2 of infinite lengths are acting on top of an elastic medium, as shown in Figure P8.6. Find the vertical stress increase at A.