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eng36-sp07-final-Li-exam

# eng36-sp07-final-Li-exam - UNIVERSITY OF CALIFORNIA...

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Unformatted text preview: UNIVERSITY OF CALIFORNIA, BERKELEY College of Engineering Statics (E36) Final Examination Problem 1. (20 points) Draw the shear and moment diagrams for the beams shown in Figure l ; (A) we 2 ION/m, o, = 1.0m: (a1) Find the reactions: {a2} Find the expressions for 17(3) and Draw the shear diagram, and (a3) Find the expressions for ﬁ/I(;r) and Draw the moment diagram ; (B) M =10 N—m and L := 5m.: (131) Find the reactions, (b2) Find the expressions for V[z) and Draw the sheer diagram, and (b3) Find the expressions for M and Draw the moment diagram . Hints: dV MM 2— r d _=V ‘ me), an dx (x) E A Milt. B O 7 (B) (b) Figure l: A simply supported beam with diﬁerent load conditions Problem 2. (15 points} {1] F ind the centroid of the cross—section shown in Figure 2 and set up the centroids] axes. __ z giAi y 2‘41- :2_. Find IE with respect to the global centroids} axes. W 'rlrlltl‘o IAWIIIII’? \ \ ,._.- § Y ? e 41 t Figure 2: The cross section of e. T—beein Hints: IS = / yZdA, Iy = / ﬁrm (1) A A Is 2 [me + (FA, 4: Parallel Axis Theorem (2) M3 Lectmgugm = E <2 (The genetic formula for local centroidal axis) {3) Problem 3 (15 points) A 2.4—m-long boom is held by a ball—end—socket joint at C and by two cables AD and 3E. An external load W = —880j is acting at point A. Determine the tension in each cable and the reaction at the point C. Fig. 91.116 Figure 3: A three—dimensional structure (a) Draw free—body diegram for her AC; (b) Write down the vector expressions for rA, r3, rep = 1—D — rm and ['35 = r3 — r3; (c) Find the forces in the vector form, W, TAD, and T55; ((1) Write the vector form moment equilibrium equation, 2M0 = Eric x Fl- :0 and ﬁnd TAD and T33; (f) Write the vector form force equilibrium equation Zia-=0 and ﬁnd 01, Cy, and Cz Hint: , [1 j k er=[rx ry rz in F3, Fz Problem 4. (20 points) Denoting by its the coefﬁcient of static fric— tion between the block attached to rod ACE- and the horizontal surface, derive expressions in terms of P, as, and 6‘ for the largest and smallest magnitudes of the force Q for which equilibrium is maintained. (3.) Draw the free—body diagram for the whole system; {b} Find the ground support force As, and the ._ . friction force acting on block A; \ / {c} Find IA: 351;: and the virtual displacements it dig and 6gp; {d} VVIite down EU and let 5U = O to ﬁnd max mini Fig. moss and 1910.51 Q an Q Figure 4: Friction and Virtual Work Method Problem 5. (15 points) A ﬁoor truss is loaded as shown. Determine the forces in members Fl, Hi3 and H3. (1] Find the reactions at the point A and the point K; ('2) Use method of section making a cut, draw the free—body diagram of the remaining sub— SIructura and then solve for internal forces FF}, Fm? and PH; . 2501b 5709. lb s00 lb 3751!; 253:5 2501b r2511: 4f; mire ' ' -r—--i Figure 5; A Truss System with External Loads. Problem 6. (15 points) Bar AC is attached to a hinge at A and to a spring at the point B. The spring constant is k, and it is undeformed when the bar is vertical. Find the range of values of P for which the equilibrium of the system is stable at shown the position 9 = 0. {a) Find me in terms of 6 and (I) and find the relationship between 8 and qb when 9, a} << 1; (b) Find 3:3 and yg and write down the po— tential function for the system in terms of 8, P, k and a; (2) Show that 6 = O is an equilibrium position by using the equilibrium condition dV _ a9 _ U ; (3] Find the range of values of P such that dQV (£92 the equilibrium at 6' = 0 is stable > 0. Figure 6: Equilibrium of a two—bar system. ...
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eng36-sp07-final-Li-exam - UNIVERSITY OF CALIFORNIA...

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