Proble (0 ponts): The plstc block shon s bonded to rgd support nd to vertcl plte to hch 0 kp lod P s ppled. Knong tht for the plstc used G = 50 ks, deterne the deflecton of the plte. Gven: G 50 ks, P 0 kp, densons Requred:? plte..8 5. n Soluton: sher P 0000 90.5 ps 5. sher 90.5 0.0 G 500 0.0 0.05 n plte δ = 0.05 n
Proble (5 ponts): To sold steel shfts (G = 77. GP) re connected to couplng dsk B nd to fed supports t nd C. For the lodng shon, deterne () the u sherng stress n shft B, (b) the u sherng stress n shft. Gven: G 77. GP, d 50, d 8 B 0., 0.5 B Requred: () B, (b) Soluton: T s chosen s the redundnt force: T T J d.590 T T 00 J d 0.70 T T 0. 9 B B B 9 B B B / 9 GBJB G T.590 00 T 0.5 B/ C B 9 G J G 0.70 T G T 9 G 0 0. 00 0.5 / B B 9.59 0 0.7.7 0 9.55 0 T 0 T 05.0 N. G T c 05.00.05 T T N MP B B B 05.0. B 5.0 9 J B.590 9.90.09 T c T T N MP 00 9.9. 7.7 9 J 0.70 τ B= 5.0 MP, τ = 7.7 MP
Proble (5 ponts): Wooden bes nd steel pltes re securel bolted together to for the coposte eber shon. Usng the dt gven for ood nd steel, deterne the lrgest perssble bendng oent hen the eber s bent bout horzontl s. Wood Steel Modulus of Elstct 0 ps 9 0 ps lloble Stress 00 ps ks Gven: E ps E ps ps ks lloble lloble 0, 90, 00, s Requred: M? Soluton: We hve coposte be. The steel re s dened n the horzontl drecton nd trnsfored nto n equvlent ood re. Snce the re s setrc th respect to the centrl horzontl lne, the centrod s locted t the horzontl centerlne ( fro the botto fber): Es 90 n.5 E 0 b nb.5 5 7.5 n s trnsfored s 5.5 n 0 7.50.5 7.50.55.5 99.8 n 0099.8 lloble M c lloble trnsfored M 09.9 kp. n c 5 trnsfored 00099.8.55.5 lloble nm c s s lloble trnsfored s M 89. kp. n nc trnsfored M n M, M 89. kp. n s M = 89. kp.n
Proble (5 ponts): For the be nd lodng shon, consder secton n-n nd deterne the sherng stress t pont. Gven: the propertes of the cross secton, lod confgurton Requred:? Soluton: The be s loded setrcll: R R 90 KN B The sher dgr shos tht sher s constnt cross the to sectons C, nd CB, nd equl to t locton n-n. V 90 KN We need to deterne the locton of the centrod, nd the centrodl oent of nert frst. The sherng stress s deterned net usng the follong equton here the frst oent, Q, nd the thckness, t, correspond to pont : VQ t 90 V + _ -90 Secton ( ) ( ) ( ) 90 00 88000 0 00 000 0 00 000 Su 00 000 000 5 00 00 0090 5 080 000 5 z z d 5.80 5.80 Q 0 0 90 5 80 80 t 0 0 0.0 5 The reson h t 0.0 s becuse the other portons of the lne pssng through re stress free. f pont s locted slghtl upper thn here t s no, t 0. 5 9000080 VQ 0.9 MP t 5.80 0.0 τ = 0.9 MP
Proble 5 (5 ponts): For the stte of plne stress shon, () deterne the vlue of τ for hch the n-plne sherng stress prllel to the eld s zero, (b) dr the Mohr s crcle for the correspondng stress stte (σ nd σ gven n the fgure, nd τ clculted n prt ()). Gven: MP, MP, 0, 5 CW= 5 eld Requred: ()? (b) the correspondng Mohr s crcle Soluton: prncpl plnes. Therefore: should be such tht the rotton of 5º CW brngs the sste to the p tn tn 0 tn p.88 MP The negtve sgn represents tht the sher s n the opposte drecton copred to the postve sgn conventon. Net, the Mohr s crcle s drn: vg 7 MP C @(7,0) X @(,.88), Y@(,.88) R.88 5.77 MP τ X (,.88) θp C (7,0) σ Y (0,-.88) τ = -.88 MP
Proble (5 ponts): For the be nd lodng shon, deterne () the equton of the elstc curve of the be, nd (b) the slope t end B. Gven: lodng nd support confgurton Requred: ()?, (b) B Soluton: The rectons re deterned frst:? 7 M 0 : RB 0 RB F 0 : R RB 0 R The bendng oent equton for the hole length of the be s deterned usng sngulrt functons b kng cut n the secton locted furthest to the rght (). t s ssued tht dstrbuted lod of ntenst ests on the hole length of the be, nd dstrbuted lod of ntenst s dded on porton of the be: M cut 0 : M R RB 0 d B E M R R d d R RB E E C d R RB E C C R 0 0 : 0 R R R B B B 0 : 0 0 7 E d 7 d E 8 8 7 B E 8 8 0 C 0 C C E C 0 C 0 R 0 C 0 θ B = E
Proble 7 (5 ponts): Colun B crres centrc lod P of gntude 5kps. Cbles nd BD re tut nd prevent oton of pont B n the z plne. Usng Euler s forul nd fctor of sfet of.5, nd neglectng the tenson n the cbles, deterne the u lloble length. Use Gven: P kps E ps F S 5, 9 0,...5, 8 n, 0.7,. n e e E 90 ps, 8 n,. n. Requred:? P P F. S. 5.5 7.5 kps Soluton: cr e e 90 8 E Pcr 7500 7.5 n 90. E Pcr 7500.9 n 0.7 n,.9 n =.9 n