6.11 Determine the force in each member of the Gambrel roof truss shown. State whether each member is in tension or compression. 300 lb 600 lb Ba 600 lb D E G 600 lb 2 ft 4 in. 300 lb 6 ft |-8 ft- -8 ft 8 ft- -8 ft 8 ft- Fig. P6.11 1 I. EXTERNAL FORCES: APPLIED LOADS * REACTIONS AT SUPPORTS. ASSUME DIR. FOR REACTIONS. Fx =0 = RAX .. NO EXTERNAL HORIZ. FORCE COMP. -300-600-600-600-300 + RA + RH+ EMH = 0 ==' RA 2400 'b. -RAS = RA+ RH (32') + 300* (32') + 600 * (24') + 600 * (16') +600*(8) # = 9600'" + 14,400 ' * + 9600"" + 4800"* = 1200 = R 32' CONSIDERING SYMMETRY, APPLIED LOADS = 2400*1 2 REACTIVE FORCES EQUI-DIST. ACTION 2400*1 1200* | R = 120 FROM CENTER = REACTION = 2 REACH REACTION = 1200* | JT.A 300# FAB FAB A FAC 8' 16+8=10 1200* 1200' - EFX = 0 = 4 FAB + FAC = PROB. 6.10 cont'd. 2 of 3 FAB 4 FAB FABY FAB EF =0 -300 + 1200 - FAB FAC = FAB = 1 (1500*), FAB = 900 (5) = 1500" 16. COMPRESSION. JT.C F = 1200 C TENSION AC JT. B FAC = 1200%. TENSION. Fac = 0, BY OBSERVATION & Fx =0 = FBc FCE 600* MEMBERS BC and FG are ZERO - LOAD' MEMBERS. EF=OFFEF=FAC = 1200%. + FBD 12=4" 100 128" OR FAB-1500* COMPRESS. F =0 BC M 4 F 8' BE 96" 28+96-100 EF-0 = 4 (1500*)-4B-16 FBD 96 F = 0 = - 600 +33 (1500) - 28 F BD 100 + Fes BE TENSION. 28 96 =tan = tan 28 = 16.26 96 1 and 300 + 675 300+BE = 28 FBD SOLVE SIMULT 900 = 1 100 4 FDE = AL FOD x 3/ Fee 28 FBD 100 4 FBD = 975* COMP. FBE = 12 Feb 100 then 975 100 = FBD FBE = [28 (975*) -300*] 100 FBE = -45* = 45* TENSION. ASSUMED WRONG DIR.! JT. D FBD=975* COMPRESS. EFX = 600* 0 28 FDE ? FDF 96 PROB. 6.10 cont'd. FDE has same FDFX = 96 FDF 100 28 FDFY = 20 FDF Fory= 100 COULD BE A 'ZERO-LOAD' MEMBER. = 0 :: FOF + 96 (975 *) - 96 F = 0 100 100 DF EF = 0 = 600* + 28 (975 *) + 28 FDF JTE FBE 45" - 100 -600 + 273 1FD = 54* COMP. DE -54 = 'slope' # 3 of 3 as FED BD 975 COMP. + FE 273 = -FDE = -FDE :: FDR = 54%. DE COMPRESSION DUE TO SYMMETRY You CAN ASSUME FEE = 45* TENSION FEE = FEE F= E = 1200' CE TENSION E EG FEG = FEE = 1200* TENSION. CHECK - EF-0 -1200 (45") + 4 FEP + Fea EF-0 " - 1200 - 4 - 3 (45*) 54* + 33 FEF 27-54=- FF - 36 + (45) = -FEG .. F = +45* TENSION EF :. F = +1200# TENSION EG