Question

20:51 43601_Assignm... QQ. 18% ; Question 1 CORRECTED [25 MARKS] Figure 1 shows a parallel chord truss of span 4 m and depth 3 m. Take E =200 kN/mm². The tension members all have a cross-sectional area of 2000 mmand compression members have an area of 2500 mm. Find the vertical deflection and horizontal deflection of the joint A due to a horizontal (-) point load of 125 kN acting at A, and a vertical point load of 50 kN acting downwards (1) at A. (In your solution follow the member labelling (1) -(17) as shown in the Figure) (17) 3 m (3) 4 PANELS @ 4 m = 16 m Figure 1

Answer 1

ta 97 14 try to Y256 Xh B1 16m 50 kn - {fy zo 3 E MAZO NA 250 kn 50 x 16 + HB x3 - 125*3=0 Epi-141.67 (-3) HA = 125 + 141.67 - 26667 kN (6) E Faso = P forces: PG = Pazo Piy= 50x5 83.33kW PS : [25-83.33* 4 = 58.34 kW Prz + 83.33 X 3 = 0 -> Piz? - 50 kn - 83.33x4 - 66.66 KN, Piz = 50x5783.33 AN Puz 58.34 – 83.33 o 4 2-813460

Pic = -83-33* * = -50 kn 2 +83.33 (N 5 2 + 50 25 IN P. = 28.3405 - -8.34-83-33% 4 15 Pa = 66.66 +83.33*4 = 133.39 kn Pic : -83-33 x 3c - 50 kw PL = 50x5- 83.33 kW Pa = -141.67 kw Piso Pio = 266.67 – 83.33*4= 200kr For finding horizontal deflection at jont" À 1 Applying unit load at A in horizontal direction 2 97 199 8 Ire ta Kre к,, к, го Kig 20, K5=1, K1=0, kg =0 K is to, kq = 1 kN, Kibao

kiz* 0, K3=1; Kq - 0, ks = 0 , K10=0 K, 20; K, 20, KPI Horizontal deflection at A:- & Pkl for all members, | AE 'K=0 for all members expect 2,3,4,5 members. L= 4m for 2,3,4,5 -75*1x 4000 - 58.34 x 1x 4000+ (An) - 58:34 * 10.50 -8.391 4000 + 2500 x 200 2500x200 2000 x 200 -149.67 * 1 *4000 2500 x 200 z ..-1-207 mm a (deflection is opposite to load applied in a KN) For vertical deflection at A: u 115 116 LW

eft KG - Kp 20, kly - 5 KN, kas in K, 2-1kw, Kis Takm), Koneen Kaza: Kik 2-1 EN.' is KR = 5 kn, kq = 8 kN, Kz? =4 KN, kis = .-1 kN, k,,= 5/kN ,K, 20 ka = = 5.33 kN , Ko= 4kn

A . Vertical member deflection P at K (-) A22500mm? for Comp (+) A = 2000 mme for tensial PKL L (mm) LAER. 3000 4000 -141.67 -5.33 6.048 4000 2.4 -75 -8.34 -4 8 4000 . 0.178 58.34 4000 -0.778 . 0 66.66 3000 4000 4000 0.888 133.33 4000 3.555 ono hoitooo er r s ķe A1 200 ...o sim caly s wolny kolm with an 4000 1.736 83-33 83.33 5000 5000 1.736 1 83.33 5% 5000 1.736 5000 1.736 : 03 83.33 -50 250 -50 : 1-1 - -1 ī ī 3000 3000 3000 0:3 0.3 Towards Low Spec28.435mm (1 EPKL 28.435 mm - AE hotels in applied unit load)