Question

(Anker ALL questions 1. (10 marks) Fig. 1-1 shows a statically indeterminate truss under a vertical force of 20 les point A and member 1 is was made 0.01m too short before it was fitted into place structural stiffness matrix is given below. Structural Martin -55 166154 0 -830.77 553.85 -830.77 0 738.46 553.85 -369 31 -55 -369 -830.77 553 85830.77 -553.85 553.85 -369.23 -553.85 369.231 0 -830.77 -553.85 0 830.77 553.85 -553.85 -369.23 0 0 553.85 369.23 a. Determine the nodal displacements at node A. b. Compute the member force in member 1. 6 (unit in kN/m) (6 marks) (4 marks) 2m 20kN 3m Fig. 1-1 Statically indeterminate truss

Answer 1

Ans (6) for redal displacemat at A In the giren figure as the points are no displacement S3, S4, Ss & So=0 fixed to there will be Hence matrix keill be Structural Matrix esco año com o As 83, Sy, Ss & Go to hence it will reduce to 1661.54 Lo o Tsirror 738.46 8₂. [20] 738.46 on & Solving 8, 0 738.46 S₂ = -20 - 82 = 0.027083 meter

As to it we have o.olm will affect as initial displacement or shortening displacement in dign 1 & 20 Such that - As anos for o Sin o= P Caso = B = 3 hence Sino = 2 = Si 0.01 - s = 0.00603022 m =0.00904534 m Coso= - VT 0.01 vet displacement at node 1 in dion 1 - SI = 8,+S,' = 0.0000 4534 m in dish 2 - 8 = S₂ + S₂ = (0,00603022 to0027083) = +0.03311369 m the sign indicates opposite dirin

for force in Pia E, AI member i S-li-m, l, m, ] | Sz usu thandustum, In both element or E, A = this we 1 2 2 Ez Az are assoming the E, A, for are soma l & also la = lez =VI To find value of J les 0,= 180-2 = 180 - tant (2) = 146.3° & 02= 33.7° b = in cosoi = -3 & mi= sind, = 2 / l2 = Coson - 3 2 m2 = sino2 = 2 BREAL! - 1661.54 ) - 10150385

* Piz 1015.3855 12 2 10.00904534 ? 3] -o. 1.03311369 1 1.9678 KN

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