d = 15 mm W L = 2000 mm h = 150 mm

The figure below shows a section of a column subjected to load P, which is applied 50 mm from the midline of the section's web. The column is made from material, which has an allowable normal stress of 180 MPa (both in tension and compression). The area of the section is 10050 mm?; the principal moments of inertia Imar = 146.554x106 mm and Imin 20.076x10° mm*. !! Determine the maximum allowable load P. 15 mm 150 mm 15 mm 150 mm 50 mm 15 mm 100 mm 100 mm 1194.6 kN 363.6 kN 1809.0 kN O 516.4 kN O 189.5 kN

A steel torsion bar AB with diameter d = 34 mm, and ductile material of tensile yield strength Sy = 276 MPa is attached to a rigid arm at A, supported by a bearing at C, and fixed at B, as the picture shows. At the right end of the arm is mounted the wheel on which the vertical force P acts from the ground and which passes through the center of the wheel. If bearing C acts as a simple support and the effect of transverse shear due to P is negligible, determine the maximum force P (in kN) that can be applied to the wheel. Consider a factor of safety n = 2.5. Use the maximum energy of distortion failure criterion and do the analysis on bar AB (torsion bar) in the section where the bearing is.

The figure illustrates a torsion-bar spring OA having a diameter d = 12 mm. The actuating cantilever AB also has d = 12 mm. Both parts are of carbon steel. Use Castigliano’s theorem and find the spring rake k corresponding to a force F acting at B.