MECH 320 Midterm, Spring 2012

Name: ID#: Sec#: Problem 1(15%) Beam (ABCD) is subjected to a uniform load w (N/m) from A to D and a concentrated force P=w.L at B. The support at A is a hinge and a roller at C. a) Draw the shear and moment diagrams. P=wL a 5ML= : L wih [-250L Shear Diagram Moment Diagram Name: ID#: Sec#: Problem 2(10%) Bracket A-F, located in the xy-plane, is fixed at F and subjected to loads P, 2P and 3P at A, Band E, respectively. Distances AB, BC, CD, DE and EF are all equal to L. The loads at A and E are along the z-axis and the one at B along the y-axis. Bar AC is along the x-axis and CF is along the y-axis. The angle between the x- and y- axes is 90°. a) Determine the internal forces and moments at D and show their directions. z -2PL= Mpz } P = Dz ral . ot vy Mpy = -2Pl MDy = -PL Dx=0 4am on" T. aing Pa a Ce ee 6.366 HPa Fy et ee 7 - 16.28 xt0” trad 4.41410 rad —— Gains a a aa 3.39 MPa T(r = Tar (2wt E) arn? (wb) Ages©& fark G fer (2wt £) L = ” (at) L L Name: ID#: Sec#: Problem 5(25% A beam, with cross section shown below, is subjected to a moment M of 6 KN.m with direction as shown. The cross-section is symmetric with respect to the z-axis. a) Determine the maximum tensile and compressive bending stresses and their locations on the cross-section. \ 12 45 i oe Eo 75 M 250 wv — er Ttep ~ 34.277 x 108 tr, - bxt0% x (262 - 6f.701) - 31.03MPa (c) bet 34.277 X10