Question

Chapter S4, Problem S4/018 The signboard truss is designed to support a horizontal wind load of 725 lb. A separate analysis shows that 5/8 of this force is transmitted to the center connection at C and the rest is equally divided between D and B. Calculate the forces in members BE and BC. The forces are positive if in tension, negative if in compression. 5.5 725 lb 5.5 F /B 6.0' 5.5 6.0' 3.0 Answers: BE = Ib BC = Ib

Answer 1

Sole force transmitted at point c (fe) = x125 453.125 lb Force transmitted at Point 'B'and D FB fp = 3x725 = 135.94 lb - X 2 Free Body Diagram of Point 'D' fo calculation for o FCD FDE ADCE and ADBE is similar triangle So, CE BE DB DC - => CE = 6x5.5 11 31 therefore СЕ tano - 3 5.5 DC o = 28.61° Free Poody Diagram fo 28-61 FDE टिक

Applying lami's theorum we get FD FDE sino sin(210) FED sin(90-0) 135.94 sin (28.61). FDE sin (270) fco Sin (90-28.64 on solving we get FDE = -283.89 lb (compressive in nature) and fcd = 249,23 lb Free Body Diagram of Point 'el foc Equating the Hoxizontal and vertical forces weget fo ELE Foc = FBC = 249.23 lb FBE and fc = -fce FLE= 453.125 lb compressive) FBC = aug.23 lb Tensile Nature]

Free Baly Diagram of Point 'E' FDE here 1 190-0) HE BC tunda FE СЕ FER 5.5 tanda 3 FIBE fo = 61.335€ Resolving the forces in Hoxizontal and vertical direction FDE K 61.39 Fee 67.39 128.61 1 For FBE FoE sin (61039) GE 605761.34) E Fer sin(28.61) विह FBE Costol.30 Fere cos(28.61) FBE sin(61.39) + Equating the Horizontal and vertical forces we get

EDE Co S{61:39)+ + F C G + For Cos(61.39) = F Sin (28.61) EF Put the value of FE and Fee we get – 283.89x6361.39)+(-453.125)+ FRp. Cos (61.39) FEE sin 68.61) - 3170186 + 0.478 EBES 0.478 FEF 0.478 (Pre-Fer J = 317.186 FBE - FER 662.398 lb - () Equating the vertical forces we get EDE sin(61.39) For Cos(28.61) + Fe sin(61-39) EF BE -283.89 x sin(61-39) - Fer 60 $28.61) + fpe Sin(61.39) 0.878(FeF+ FRE) pug.23 OY FRE+ Fer + 283.894 - lii)

on Solving Equation (1) and (in we get FER = -473.146 lb And And FBE 189.252 ello to (Tensile nature]