MECH 320 Final with Solution, Spring 2010

MECH 320-Mechanics of Materials AMERICAN UNIVERSITY OF BEIRUT STUDENT NAME: ID: Spring semester 2009-2010 Instructors: Shehadeh M., and Nasser-Eddin M. TIME ALLOWED: 2H Problem 1. (25pts). The two-bar truss ABC shown in the figure below has pin supports at points A and C, which are 2.0 m apart. Members AB and BC are steel bars, pin connected at joint B. The length of bar BC is 3.0 m. A sign weighing 5.4 KN is suspended from bar BC at points D and E, which are located 0.8 m and 0.4m, respectively, from the ends of the bar. Determine the required cross sectional area of bar AB and the required diameter of the pin at support C if the allowable stresses in tension and shear are 125 MPa and 45 MPa, respectively. (Note: The pins at the supports are in double shear. Also, disregard the weights of members AB and BC). Caladation 4 Rey cued Ray (Pg b) SE Hp co Ry, (Remmmh 4 (24 EN) 4 QAM br x 2Qom ; _ reas coloration fe Re= TR iReuS= > | = _ 2 siZeN “Tense feces in ben PDs Thy = Bee ° | _ 5, ISkKN - Problem 2.(25 pts) A horizontal rigid bar AB is pinned at end A and supported by two wires CD and EF at points D and F as shown in the figure below. A vertical load P=1.5 KN acts at end B of the bar. The bar has a length =3b. The wires CD and EF have length L,=0.40m and L.=0.30 m. Also the wires CD and EF have diameters of 4 mm and 3mm respectively. The wire CD is made of aluminum with E4i=72 GPa while the wire EF is made of Magnesium with Eye=45 GPa knowing that the allowable stresses in the Aluminum and Magnesium wires are 200 MPa and 175 MPa respectively a-Calculate the normal stresses in bars EF and CD. adequate. —b-By-reference-to-the-values-found-in-part-a; determine if the materials used-itt “the design are . ~& = = Bx lsxte ( ©. 4431 x lo a ee: lexo. 42 x lo pase’) [24.4 Mi . p 2 OHIO \ Vo= > Je. Gx io xlo (— lor corre Tq’ >Varnig ; 7 As foe oty On Problem 3. (25 pts) Four gears are attached to a circular shaft and transmit the torques shown in the figure below. The Allowable shear stress in the shaft is 70 MPa. a- What is the required diameter d of the shaft if it has a solid cross-section? b- Another design is suggested such that a hollow shaft of an inside diameter of 40 mm and an outside diameter of 60 mm is used, would the shaft sustain the applied torque ? Justify your answer. t aly = Yom Pa Draw dhe joven Ces hone aw SZ . . TI: Ty ee Ke Qh. My = Rw ve) xle om u A y Jt Ec del FS) = at U6 Sz tots xhs mee ra BO x\S° _ =F C= 126@sbex's 2 35.26 MR x le e2t ie & The shel asorX) susteth We aid sor Qe pece C poe < ere D> ¢ (2% OP Est A, Gy Au Ext fat 3 -~& 2 As = Se Cloxt®) = FES XLET oe 5 mm Aal = C 3 i ee = Yos. 6 vlc 7 So = 2xet «we Lexy 9.5 yl izvasalow ° : G ‘ . A r “ 28 x, Te oe EPI —" Fett Fs 6h Fort Rama - ac Los 2 oe => oO. b66f574 + ©.606 2e2 4o.dooe F24EL be Mex: Toca Shen: 2D See re sveok wa Aes Bethe ~ Oyys5 se ew cand Sas many mw foal) Orne — PP is seo ef on > ina Paar Wek ps SHED wt be induced) Move - & - al . Troe = AES = 954.65 MP _ -3 2 a. VW" SE Vent?) Ld - ‘> <3 c- GO EG >aeE- F = 2H 6S. hey xls 5h sy ‘oom ne) - Qos ve ye 2 Sey su, Ey -CoCrayye . San 11 ; - Zp ‘ ep = 0 382 xle = = 3 _ ~3.§2 xo mre sD = C 6 4X Gx Ue a