Question

Question 2 (15 points): Tension, Compression and Zero-Force Members in a Truss Structure. Consider the truss structure shown in Figure 2. 3P (kN) P (kN) I LI LL Figure 2: Elevation view of 27 bar truss structure. Vertical loads of 3P kN and P kN are applied at nodes B and D, respectively. [2a) (3 pts). Compute the magnitude and direction of the total support reactions at points A and C. [25] (3 pts). Identify the zero-force members (If you wish, you can simply annotate Figure 2). [2c] (7 pts). Using the method of joints (or otherwise) show that: (1) The maximum tensile force in the structure is 2P kN (T), and (2) The maximum compressive force in the structure is -2V2 P KN (C). [20] (2 pts). Draw a simplified version of Figure 2 with all of the zero force elements removed.

Answer 1

2Fx=0 se Zfyco уче че EM=0 alout it cy (3L) = P(BL) +3p (4) c. 2p. 10 2. Ay= up-apooplen. 10 b) zero force members are as shown in the above terues. 3 At solut A2 At jourt at FAG = FOR = 2221 INC) At jo fint. Hi FAW = FBH =2P INCTS FAG sinus=2p FAG = 2820. ks. (c) FAH = 2528 colus = ap kN CD At joont F 3P At Jodet Ne FNE - AG forutin INE =pkoce) The N 2620 FIF & FBI place fif sinus-3p-22 2p sinus FIF / 2 P KN (c) fulf = 262p Lorus- Sap casus - p. ko cc FRJ=o. At joonty: FIE - At sorut kr FER & At joint ! Af Joint & FRO=(2p.(c) R a us S2 P FIE sinus + FRE Sinus = P. P. FJE COSUS - FIS cou5=up. - FJS = 0 FIE = 2pcs Atjoint o: Foo FBO = 20 G) for sinus- Sapsinur = FOL = 2pco FDO = 262 p cosur - 2P (T) Atjodut Li- FOL= FEL= S28.(c)

At joint ct M o l. At joont ut FBM Fomo sap con Fom cosus-Safcoug 28. Fome sap LN (c) e. Marionn Tension = 28 ko which is in AHIBH, DO, BO Mammum Compression - 2220 kn which is in AG, GF Pko do - FBPKN. 1 pko