The cantilevered handle in the figure is made from mild steel that has been welded at the joints. The lengths are a-7 in, b-7 in, and c -2.5 in. For Fx=0, Fy=275 lbf, and F₂-0. Use Castigliano's theorem to determine the vertical deflection (along the y-axis) at the tip. Note that when calculating the torsion strain energy of a noncircular cross section, Jis not the polar moment of inertia. Instead, use Eq. 3-41 to determine an equivalent Jeg for the solid rectangular cross section of member BC. The vertical direction at the tip is 1-in dia tin in. in dia.

The stress tensor in MPa for a three-dimensional system for some x, y z axis system is 20 40 -301 40 30 25 -30 25 -10. (a) Confirm that one of the principal stresses is 65.333 MPa, hence find the other princinal stresses and the direction cosines of the planes on which they act. (b) Determine the maximum shear stress.

5. A long slender column ABC is pinned at ends A and C and compressed by an axial force P (see figure below). At the midpoint B, lateral support is provided to prevent deflection in the plane of the figure. The column is a steel wide-flange section with E= 200 GPa. The distance between lateral supports is L = 6.0 m. Calculate the allowable load P using a factor of safety n = 2.0, taking-int- account the possibility of Euler buckling about either principal centroidal axis (i.e., axis 1-1 or axis 2- 2). Use Table F-1(b) in Appendix F (attached) to find section values. X B A ======================= X L L 2 W 250 x 67 Hi 2 Section X-X

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es A gear reduction unit uses the countershaft shown in the figure. Gear A receives power from another gear with the transmitted force FA applied at the 20° pressure angle as shown. The power is transmitted through the shaft and delivered through gear B through a transmitted force Fg at the pressure angle shown. For the steel countershaft specified in the table, find the deflection and slope of the shaft at point A. Use superposition with the deflection equations in Table A-9. Assume the bearings constitute simple supports. In the figure below, FA is 310 lbf and the diameter of the shaft (dshaft) is 1.29 in. dshaft Gear A 20-in dia. 16 in FA 20⁰ The deflection at point A is The slope at point A is 14 in 100 Gear B 8-in dia. rad. 9 in in. B FB 20°