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Practice Midterm 2 Sol

Practice Midterm 2 Sol - £x V£y_E3y y5x V ax‘ I‘VZ...

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Unformatted text preview: _ £x+V£y _E3y+y5x _ V ax‘ I‘VZ UY— 1_V2 £Z_—1_V 52 = 0 Ex: ‘EL<6x-'U€'J) , CH '5‘): -E‘.-.-(-1/6,(+65/) Mup'l'ipp/{nj (23 Ly 2/ amJ Mai/34:1, +0 m _ Z (Ex-Fiji); = ‘E'ZJ 6; CW GX=I_E7;,1(E,¢+ 7J8?!) Muﬁwﬁwa m LY 7) cm! MIA"? +om \ -vL — , 5741/8). rig-6:] OV‘ gtlfszS‘Y4-y8x) 92 = —E'—(—v6’,— 2263} = _§./-fvz( E, +vsj + EJ, + y&,) - -—>iJ£_L’§-ffl(sx+ £3: =' -%(s +3.3 Ca.) Ska AB .2 TAB : 3.6 x103 [5,!“ c = éa. -— ans) = 0.65m. “ —" QT J: ate? 2;”: LS -_— _._ / J , was _ (7—! 6.64103) _ 3 ‘ 3.9 kcpvin ‘ ' ‘ ’Z’m — 7710.65? .— 23910 P“ 2:91:75 : g. 35 k5; (b) Ska-Hr 8C: Te = éjxlc)’5 454.4 C A -r V c=éJ=-9{(f.8)foﬂm. :irc." QTec (73.6 8x103 _ M : —-—~ — ' lo ‘ (mum. TCS ~ T((9.cl 33 5.?‘fx P5 Q Tcu: T; 2" 100:) “‘3‘”. _ V1 ‘0 ‘ ’1’ ~ .1. -. LN.“ “-37:75 :2 , T: 10GUN-m 723 - 7:37:32 ﬁClooo3~ 2500 Now. . . .. .. D For (Jestﬁn Based on S+MSSJ USE IN .2; pom/39" +OY‘7UC4 TAE Z; 2500 Nam. 400mm f: IA _ 2T J — 7&3 600mm T ’2.) a \ . c = 29.82xlo” m = 29.32 Mm) a = 2: = 57.é mm Design based" on ho+a+iom anﬁﬁz (P0 = {.56 = 26.!8x10'3mJ Ski}?- AB: Tm = 1.500 N-m ) L= 03+ m @ = IL- : 2570’ng 0.42 _ |OOO AB Gd- ' GJ’ _ GJ- = = moo - Gems (P8 (FAB (,3- ' = Y‘e : £39“ 1000 __ 2500 49¢ 7‘: 4’5 0 GJ‘ GI 13th co 71° - I000 MM) L= as m (p 7: 1:1: 000) 0*; _ _____GOO CD GJ‘ GJ GK? 2 —: 250° .622 _ 3/00 - 3/00 Q!) q): '+ (pct; re"; + G— ' 9‘3“ " W (mCSIoo _ 2 an») ‘ 5‘: ‘ » __ -‘I 4 C 7T 6’ qoa wr(77>qo‘7p(2c;.lsxto‘3> 37106 x lo M - 43 . ' C. ‘ 3}.L"é )‘Io .M :1 31-46 MM ) d = 2C = a.q mm Design mus; use. pay-Aer Vaﬁue -Fw~ ‘J‘. 0! = 6231 mm .4 L/ For the concrete beam shown, the modulus of elasticity is 25 GPa 0 concrete and 200 GPa for the steel. Knowing that b = 200 mm and d = 450 Run: using an allowable stress of 12.5 MPa for the concrete and 140 MPa for the 8’ determine (a) the required area A; of'the steel reinforcement if the beam is? balanced, (b) the largest allowable bending moment. ‘ _ E5 — 20—...“qu :' n — E; - 25y10‘1 8.0 5 ___ nMéd-xl 6;: Mx ‘5 I I G n (51—50 i 6% : ”—7“— : V1 >< ' n i' _ _\-€ - _L.______..."’°"’0‘ : '3?‘ l + v: 55: ' I + 8.0 mswoe 2’40 y, = o Luce? d = (mamaxqsm = l87.5 Mm Load: med'iﬁMuQ Wis. ima§ —. n As (ol—¥\ (a) A 7 ”L: M -: IQ7L} mm: (a) Asrlé7qu2< 5 Zn (cl—>0 (23(8.0)(292.5) I = it: x3 + to As (al’XT-7 éC2003(I27.5)3+ (aotmﬂnzezsvz = 1. 3:23 x10” m” = 1-3523 x ro‘z’ m“ I Hy Conan/wife: Hr: LO ,j: l27.5mm= 0.}875’m 6:12.5xlo‘Pq M - ___——————-————-—("2"’7‘3"’°-5w2'§¥'°‘) -_— °!0.8x103 N-m ' (Loxonwm Stu/Q3 n: 8.0 3: 2.41.57“ . 0.2“an 6':- Hovlo‘ Pa. M .W ._. magma“-.. . (2.0)(o_ XeZS\ No‘l'e Hm‘l lac-'Hx Vague: are. *HuL same l2)» Eda/wee) plasfan, 1 (El M: 70.3 kw~m ‘4 ...
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