Question

2. Draw the moment diagram for each member of the frame. El is constant. All members are axially rigid. Use the stiffness approach 30 kN-m 100kN 3 m 4 m 5 m

Answer 1

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Zolution 30KNM lookN 5 m . We have to Use Stiffness Approch. Stipt: Valculation of Degue of Kinematic Indeterminacy Dk = 73=4 ich we consider, all the Dk = 4 members inextensible Step2. Step 38 OB, OC, OD, A Calculation of Eiged End Moments MB = MEA = MCC = ME B = M D = 150 = 0 End conditions and Joint Equilibriom Eq". 10) McB + McD = 30 10) MBA+MBC = 0 10) Moc = 0 (0) Shear Equation MABAMBA + MCD + MDC + P=0 ho LAB

Step 4. Slope Deflection Equations- (6) MAB= MA REI [ 2017 OB 30 MABT ZEI MAB= 0 + GEI lo OA-o because Support Ais fixed MAB = 0.5E10B - 0.375 EIA 4. lo Mena mém + 2£1 [ 0nt208 - 34] Men = 0 + REI [0+ 206– 3,4] MBA = EI OB – 0.375E18) (0) Mec = MEC + 282 [ 206+ bc - 3A] (i hore D=0) MBC = 0+ RED [206 +0 -03 MBC = 0.8 E10B + 0.4 E3 Od Meg: NCB + 2€8 [00+200-34) 20+ 2 E] 0.4E Mcp = 0+ 22 ( 98 +282 -03 Mcp = 0.461 00 + 0.8 €10C 10 McD = MED + 2 EI [20c + OD - 30] McD = 0 + REI [200+ 00 - 30] L 1

Med = 1.34 EI Oct 0.67 E IOD - 0.67EIA (0) Moe = Moe + 2E2 [ Oct 200 - 34) Moc = 0 + E3 [Oct 200-30] L Mpc = 0.67 EI Oc + 1.3461 Op -0.67EIA Step 58 Applying End Conditions (6) MOC=0 0.67 EI Oc + 1.34 EI Op = 0.67 EIA 10167 € + 1,3400 = 0.674_ 10 MBA+MBC = 0 E108 – 0.375 E3D4 + $0.861687 0,46 10%=0 11.8E1 08 +0.4EJ Oc = 0.375E14 i) (0) McBt MOD 30 (0.461 OB+ 0.8 EI 01 } + $1.34€10c + 0.676100 - 0.67 EIA} = 30 0.4E I OB + 2.14 EI Oc + 067 EJAD 1 =30+ 0.67 EIAL (0) & = 100 MABA MBA 4 McD 3 + 1.34 Eloc +0.67 El O,-0.67 ElA = 100 1.5E10B - 0.75ELA 4

4.5E10B - 225 E1 A + 5.36 El0c + 2.68 ELOD - 2.68E1A = 1200 | 465 ElOB + 5.36 E10c +2.68 E10D - 1900 + 4.93 ELA Liv Frrom equation is ui), i), liv, we get Steble Oc = – 58.65/E1 Op = - 230.26 LEI OBE – 95.129 / EI A = -519. 187/EI Calculation of End moments. MAB= 0,5E108 - 0.375 EIA = 147.38 kNm MBA- EIOR - 0.375 EIA = 99.56 KNM M B C = 0.8E1 OR + 0.4E10c MB C = – 99.56 KNM MCB 0.4 ElO pt 0.8E 10e = - 84.97 MCD = 114.99 Moc=0

Stef?? Berding Moment diagram 95'bb 99.56 95 bb 84.97 Ć 1936 84.97 99,56 se'th! BND of BC 1 srithi BND Of AB V4.99 BMD OJ CD * Note : Zign convention C.W (2) BMD = tve. bigo lonvention ACW (9) BMD=-ve