1. For each of the following beams, i. (1 point per beam) Sketch the described beam, including supports and external loa

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1 For Each Of The Following Beams I 1 Point Per Beam Sketch The Described Beam Including Supports And External Loa 1 (128.2 KiB) Viewed 20 times

1. For each of the following beams, i. (1 point per beam) Sketch the described beam, including supports and external loads. ii. (4 points per beam) Derive expressions for the internal shear and moment resultant functions, V(x) and M(x). iii. (2 points per beam) Sketch plots of V(x) and M(x). assuming that L > 0 is a constant with dimensions of length and P > 0 is a constant with dimensions of force over length. (a) A beam of length L with a pinned support at x = 0, a roller support at x = 2L/3, a free end at x = L, and a linearly-varying external transverse load per unit length, p(x) = Px/L. Hint: To compute the reaction forces at the supports using statics, recall that a distributed external transverse loading p's net y-direction force and (counterclockwise) moment (about x = 0) are given by the integrals Fyp = $"" *P(x)dx and My = *xpl)dx. Reminder: Recall our sign convention where p(x) > 0 is a distributed load in the +y direction. Reminder: Do not forget to add the concentrated reaction force of the roller support to the external load p(x) before integrating to get V(x). (b) A beam of length L with a free end at x = 0, a roller support at x = L/2, a pinned support at x = L, and a uniform external transverse loading p(x) = P(1 – H(x – L/2)) applied to its overhang (where H() is the Heaviside function, as defined in lecture).