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Midterm 2 Sol

# Midterm 2 Sol - — J]3 i\t 5x“...

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Unformatted text preview: — J... /,]3/\ . i\t 5x“ 5(5x-vSEI-D62)—~E—(6x—WG;\ ('f. /27)>‘*V\C/ a". N (a) 6}: vs; ‘1 52 E (“96? ”“557 +615 ' 5407/16; -0 + 6:): —/Z.—w—6: 52; t E z l‘Vl ﬂ 3ng M18758 M4). m4 j PM; 08 a The homogeneous plate ABCD is subjected to a biaxial loading as shown It is known that cl = m, and that the change in length of the plate in the x directiou must be zero, that is, 'sx = 0. Denoting 'by E the modulus of elasticity and by v Pmsson s ratio, determine (a) the required magnitude of ex, (12) the ratio .170 / 8,. . The shafts of the pulley assembly shown are to be redesigned. Knowing that the allowable shearing stress in each shaﬁ is 8.5 ksi, determine the smallest allowable diameter of (a) shaft AB, (b) lshaﬁ BC. (on SMH AB; 113 = 3.010515% Tm: 8.5 lcsi = 3.5xloz Psi _ E 4% .N : IE. :_ 2T .‘T’ 2C 4”“ CT ‘n‘c3 , __ 3 C3 2,9,3 : (2) 2.9403 = 0,444 a.” 7T Lw “3.534033 an: 2C '-" /; 2‘12»). 4 L/ ' 1- (M ShaH BC: TB": 6.8x1031’L-im 21%; 8.57103)”; 3 3 3 r _ ﬂan; _ _ / magma? ‘ , C ' 2722.1, ‘ Magma) ‘ 0'7?” '“' deg 2c = L547 m, A {est a, it .- .- : .— A,;. 4 33.29;“ E%_Wrﬁlen EDD/A A3 The electric motor exerts _a torque of 800 N-m on the steel shaft ABCD when it is rotating at constant speed. Design speciﬁcations require that the diameter of the shaﬁ be uniform fromA to D and that the angle of twist betweenA and D not exceed 1.5°. Knowing that TM 3 60 MPa and G = 77 GPa, determine the minimum diameter shaﬂ that may be used. A 300 N . m 509 N ~ in n bases? on dress 75 = GOX/O“ Pa. 1:9. : 3—1: ' '5}: g]: .. (ZKSOO) -e ' 3 J 7C3 7T2’ A 7T(Go x105) :- ‘ 3. 438 3110 M C 5 .20,‘1‘0>(/0.3 m = 20.40. MMJ d =1 2C 2 1+0, 8 M». = LS" = RGJBHO'st @D/c = O (p : Tabs»; _ ggoouoe) = éoo #5 GJ" ‘ GJ G-J' (pa/A :. 712L143 .2 (3003014) .___ 32.0 GJ‘ 621’ GS ._ — 9:2 -533... - (ZXGZD (QB/A ‘ (pp/c‘FCpc/g—l-qoelk". G‘J‘ "chlf ‘m‘tl" C"I :_ M r _ (9a)<é203 _ . 0 (0—9 ‘ .4 TG Cp064 7(77 y/quZG-lgxlo’s .) - ‘q5.8 x m C. 1' 2!.04 54104 M = 2LO‘1‘ mm! at : 2c :- QQ‘I MM \$9553“ musi‘ use purge» chue a? a), d = 4-2.! MM “ . LI The design of a reinforced concrete bean is said to be balanced if the maximum stresses in the steel and concrete are equal, respectively, to the allowable stresses as and (TC. Show that to achieve a balanced design the distance x from the top of the beam to the neutral axis must be d 03E: 1+ ———- o’ E c .v x: where EC and E, are the moduli of elasticity of eoncrete and steel, respectively, and d is the distance from the top of the beam to the reinforcing steel as“ I C j: <5 ”Cal—X" 5i _ 65-6.. .x Vi X h Cp__ L61 _ ELSE 7—, i“ we: ‘ ‘+E\$G‘¢ ...
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