Question

Question 3 [40 MARKS] A steel frame ABCDE, in Figure 3, is supported on rollers at A, and is rigidly fixed at E. It carries a collapse load of 1002 kN acting at B and D. The plastic moment of resistance of members AC = 200 kNm and that of CE = 100 kNm. Using plastic theory, calculate: (a) The collapse load factor of the frame. (b) The reactions and bending moment diagram of the frame at collapse.

Answer 1

0 Solution:- (3) Given that A steel frame rollers at A, land 88 load ABCDE 98 supported on srigidly bined at E. acting at B&D. 1000 KN Ac 200 KNIM. CE = 100 kNm. 1007 3m 5m tc B 30 100 um MAC MEE Mi = 200KN-M. M2 = 100 kn.m andern No. of degree of inderminacy of ID = (377) - 34 = 3* 2+4-3*3 ID = No. of possible hänge positions p = 3(4 ©©, ) No.of independent mecharasms P-ID 3-1 १ Muhaniem. blom Mechanism sway

# Mechanism @ Beam mechanism (cam ABC) HPI L 1000 MPI D o 8744 st De B MPI MP, Dik 1002 E T 30 = 53 here -ve sigo Defamation opposite to the moment/face - MP, xß– MP, XB-MP,X O – MP,x 0 + (1000) x 30 =0 30 5В 30 - 2MPIX 3150- 2MP 10 + (1000) x 30 = 16 Mp o 3000 x 0 5 MP, 375 al-O a 다. # Mechanism © : sway Mechanism 11002 S Thu MPAA SL 1000 0 0 MP2 5 - 70 ,- MP2 XO - MP2X0 + 1000 x 40 =0 Si = 40 1 2M220 40020 MP2 = 2000 @

: 3 * Mechanism : Combined Mechanism (Beam & sway MPI 1 1009 Mpi of B B MP, MP 1000 MP 0 # MP2 5B = 30 B - 50 -MD, XB - MP, XB- MP, xo – MPixo – MP2X0-MP, xo +1000 ) x40 + 1000 x 30 = 0 - MPi xB – MP2 x B-MP. XO-MP2x – MP2 xO – MP2 X0 + 700X0 =0 - 2MP, X 50 - MP,XO – 3MP2 xO – 70000 =0 1313 MP, O +3M1P2 X0= 700x nxo 13 MP, +3M P2 =7000 now, from equation ©; MP, © 3 = 200 3750 4 2.133 0 From equation ; MB = 2000 100 = 2000 a 0.5 fzoom equation ; 13 iş Mp1+3MP2 = 7000 13 3 x 200 + 3x100 = 700x0 a 1067

which 98 0 = 0.5 A 200KNM 100 KN.M SA 3m 100KN.M IVE-30KN. from the voorous Mechanisms , adopt minimum Load factor Phorom sway Mechanism} So, the load will be >>100 x0.5 50 KN JUKN. Tum ej 10 5m 50 KIV um 100 kNm Benting Moment at B + VA X5 +100 = 200 VA 20KN. VA = 20KH. 3m A ME 50KN Efv 0; VAHVE =550 VE - 30KN EFH=0 ; HE = 0 ; HE = 50km. # Shear 13160 diagram :- VTIZAZZYZZ VIH 20KN B 30 D 50KN E 50KN

+ free body moment shaporam.cooken om + 00 200 KNM D + 200KN.M C it B 100kn m E 100km plastre bending moment diagram -D 200 KN.M 100 KN-M E + 1 Dokno 006 200KN-M Combined hending moment drogēram. VDOKH -M