Question

Three bars are connected with frictionless pins to form the frame shown. The frame is loaded with a force of P = 670 lb. The dimensions on th figure are a = 7 ft, b = 5.1 ft, C = 5.1 ft, d= 7 it, and e = 9.5 ft. Determine the magnitude of: (a) The resultant force in pin B. (b) The horizontal and vertical components of force in pin D. (c) The horizontal and vertical components of force in pin C. (d) The horizontal and vertical components of force in pin A. (e) The horizontal and vertical components of force in pin E. (1) The resultant forces in pins A, C, D, and E. Enter all answers as positive values.

Answer 1

Answer Draw free body diagrams FBD 0 ABC FBD oH BDF FBD 4 CDE - Rad Rex RO 67016 Ky RAY Here, o = tani (+) = 63.43 (a) RB=? from FBD of BDF Take moments about o → EMD=0 → R${cc8(63.43)) x 10.2] = 670x9.5 → R3 = 1395.2 Ablaue Roxy Roy from FBD of BDF Efx=0 → Rg sino) + Rox = 0 → Rox = -RB Sima) =-1395-2xsin (63.43) Rox =-1247.87 Ubl Arse

AAA { Fy=0 Rg Cofo + Roy -670 =0 @ → Roy = 670 + R3 CO3 (63.43') = 670 +1395.2685(63.43') > Roy = 1792:55W Aus •Rex, Rey Take moments about it. EMA=O → Rey(a+b+c+d) – 670 (a+b+c+e)=of Reyl. 2A-2)-670(17-2) =0 RAY > Rey = 476.2 lb) – ® { Fy zo > Ray-Rey -P=0 Ray = 193 - 8 REY from FBD 4 CDS {fyzo -Rey-Roy + Rey = 0

→ Rey - Roy - Rey = 1792-55-476-2 3 =1316.35 Rey = 1316-35 16 ans EME=0 → Rey(12.1) - Rcq(12.1 tano) - Roy(+) –RDX (7tang) =0 →-1316.35(12.1) - Rez(12.1tano) – 1792-55C7) +124787 ( Rcx = 455db Au (d) Rax, Ray from FBD of ABC Efl=0 → Rcx-RB sin (0) trax=0 > Rax = Rosino-Rex = 1395.2 ($1063.43) – 455 = 792.85 IRAX =792.85% = 193.8l6 from eq ® 2 (e) Rex, Rey from FBD of CDE 1. Efx=0 -Rex-Rox + Rex=0

→ Rex = Rcx + RDX = 455+ (-12A7-87) = -79266 . Rex = -792 lb Ay Rey = 476.26b Aus from eq @ (f) RA, RC, RO, RE = 81619 Db RA = f(paral' (Ray)" = 1792-85)+(193.87% Re = prezentarea = 455]* +(316:35)" 1 = 1392.76 lb Ro=/Rok + Roý = {21247-87) + (1792.55) 1. = 2184.12 lb RE=RE at Rey = 16 792) + (476.27 =924-13 16 All the Best.