Question

Section 1.3 Statics Review Example 1-1 FIGURE 1-6 Plane truss model 2P - c = 80° a As KOA = 60° - Og = 40° B The plane truss shown in Fig. 1-6 has four joints and five mem- bers. Find support reactions at A and B and then use the methods of joints and sections to find all member forces. Let P = 35 kips and c = 10 ft. Solution: Use the following four-step problem-solving approach. 1. Conceptualize (hypothesize, sketch): First sketch a free-body diagram of the entire truss model (Fig. 1-7). Only known applied forces at Cand unknown reaction forces at A and B are shown and then used in an equilib- rium analysis to find the reactions. 2. Categorize (simplify, classify]: Overall equilibrium requires that the force components in x and y directions and the moment about the z axis must sum to zero; this leads to and R The truss is stat- - c2 c/2 FIGURE 1-7 Free-body diagram of truss model

Answer 1

Giren, P= 35 kiPS e = 10ft. OB:48 -60 OD HA 42 C/2 fve. VA Ans+ HA b Saorbo0 60 bus6o 42 bustoo 42 INA FBD Of Truss From FBD. Efx-o HA= 2P. VA +NB=P. E MA-O :. P(busso') + 20 Cosin60)- Vg e) EFy:0 Now, foom attof Law of triangres, Sin de Sin6o Sin80° 8. 8 ft. Sinde C=0•65e = 6.5ft. Erove SPn80° d=b+G-2.b.5.co5 60 °) d = 5.9 f - :- SnDA Sinop

So, from Homent equat on, PX6.Sx usbo +2P x 6.5 Sinb0= VU6). . Ne 1.45P. = 50. 75 wis (ufaared) But, NA +NB - P VA= P- V: P-).45P = -0.45P. . VA = - 0.45 X35=15.75rwies (doonward). %3D Answery Ist Party . So,total meacton at B= 50.75 KiPS. to tal eocton at A = J Ha? aNq?: Jera)+(-1S'70) - 77.75 KiPS. Ainding member fonees + jont A. FAC :-70+ FAD+ FAe.Co560-0 70 60 MFy-0. . FACSin6o1S.7 FAC 18.19 KPs F. AD I5.75. So, -70+ fAD+ 18.19 u60°0 . 7 FAO = 60.9 kips. Efy:0 : fBe Singo 50.75: FBe 78.95 kiPS! joiat B FBe 46C0 Fesb FBD= 60.48 KiPS OB 50.75 . FBD-FRe us40 -60.48.

joint D. fo. FBD= 60.48 FAD-60.9 %3D 5, there is mo vertical toree to balamee the y-direeton component of member foree Co (fo), so CD is a Eero toree member. As, Member fonees. (omswer of and fort) Member foree varue CKiPs) Member foree Nature Tensile 18.19 AC Tensile gensile lompressive 60.9 60.48 BD 78.95 BC NA.
Note : member forces acting towards the joint taken as compressive and member forces acting away from joint taken as tensile.