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Department of Civil Engineering Fundamental Mechanics – ENGG 1300
Assignment - Axially loaded structures & statically determinate structures Please submit the answers of Q6 to Q10 by 22 October 2021. Q1 (a). Axial forces are acted on a straight bar of length L = 3 m as shown in Figure 1a. The cross- section area is A = 400 mm2. Determine the axial stresses on sections 1-1, 2-2 and 3-3 respectively. (Answers: σ1 = -50 MPa, σ2 = -25 MPa and σ3 = 25 MPa) (b). An L-shaped concrete block rested on ground is shown in Figure 1b. The width of the block is 2 m. The concrete density is ρ = 2250 kg/m3. Determine the stresses at A and B. (g = 10 m/s2) (Hint: the stress along AB is a trapezoid distribution). (Answers: σA = 232 kPa and σB = 4.22 kPa) Q2 (a). Figure 2a shows a gate holding 3 m depth of water behind it. The width of the gate is 2 m. The density of the water is ρ = 1000 kg/m3. Determine the reaction forces of the gate at A and B. (g = 10 m/s2) (Answers: RA = 60 kN and RB = 30 kN) Figure 1a 20 kN 10 kN 20 kN 1 m 1 m 1 m 3 2 1 3 2 1 Figure 1b 12 m 3 m 3 m 9 m B A σA σB 2 (b). For the beam as shown in Figure 2b, determine the reaction forces at A and B respectively. (answers: RA = -36.7 kN and RB = 196.7 kN) Q3 (a). Find all the zero-force members in Figure 3a. (Answers: Zero-force members: 1, 3, 5, 6, 7, 8) A B Figure 2a 1.5 m d=3 m A B 10 kN/m 6 m 4 m Figure 2b 100 kN Figure 3a P 1 7 2 3 4 5 8 11 10 6 9 3 (b). Find all the zero-force members in Figure 3b. (Answers: zero-force members: ad, db, de, be, eg, cg, lg, fh, hi, il, kl, ki, kh, and jk) (c). Calculate the degrees of indeterminacy of the structures in Figure 3c. (Answers: degrees of indeterminacy: (i) 3 and (ii) 10) Figure 3b c g l k P a b d e f i h j Figure 3c (i) (ii) 4 Q4 (a). Determine all the internal forces of the truss by the method of joints. (Answers: FAB = FDE = 96 kN (C); FAH = FEF = 75 kN (T); FBC = FCD = 75 kN (C); FBH = FDF = 60 kN (T); FCH = FCF = 48 kN (C) and FGH = FGF = 112.5 kN (T)) (b). Compute the member forces of CE, CF and DF by the method of sections. (Answers: FCE = 1 kN (T), FCF = 1.414 kN (T) and FDF = 2 kN (C)) Q5 Determine all the reactions and the distance yc of the cable structure. (Answers: HA = 3.17 kN, VA = 3.96 kN, HD = 3.17 kN, VD = 2.84 kN and yc = 3.60 m) Figure 4b A C E B D F G 0.5 m 0.5 m 0.5 m 1 kN 0.5 m 2.5 m yc 2.0 m 3.0 m 4.0 m 2.8 kN 4 kN A B C D Figure 5 6 m Figure 4a A B C D H G F E 5 m 5 m 5 m 5 m 4 m 30 kN 60 kN 30 kN 5 Q6 (a). A column is made of two kinds of materials (M1 and M2) as shown in Figure 6a. The density of M1 is ρ1 = 2250 kg/m3, and its allowable axial stress is 2 MPa. The density of M2 is ρ2 = 3250 kg/m3, and its allowable axial stress is 3 MPa. The cross sectional area of the column is 1 and 2 m2 (upper and lower part respectively) . An external force P is axially applied at the top of the column. (i) determine the maximum value of P, and (ii) determine the axial displacement induced by P at the top of the column. The Young’s modulus of M1 and M2 is E = 20 GPa. (g= 10 m/s2) (b). A concrete column rested on ground is shown in Figure 6b. Three point loads are applied on the top of the column. The width of the block is 2 m. The concrete density is ρ = 2250 kg/m3. Determine the stresses at A and B respectively. (g= 10 m/s2) (Hint: the stress along AB is a trapezoid distribution). Figure 6a 12 m 12 m P A M2 B M1 C Figure 6b 10 m 8 m B A σA σB 4 m 3 m 800 kN 500 kN 500 kN 6 Q7 (a). Figure 7a shows a gate holding 4-m depth of water behind it. The inclination angle of the gate is 30ºto the horizontal. The width of the gate is 4 m. The density of water is ρ = 1000 kg/m3. The weight of the gate can be ignored. Determine the reactions at A and B. (g = 10 m/s2) Q8 (a). Find all the stable structure(s) as shown in Figure 8a. (b). Determine all the zero force members in Figure 8b. A B Figure 7a 30º 4m (a) Figure 8a (b) (c) (d) Figure 8b 7 (c). Find the degree of indeterminacy of the structures in Figure 8c. Q9 Find the internal forces in members AB, BC, BH, CH and HG. Figure 8c (i) (ii) (iii) (iiii) 8 Q10 Please describe two general approaches for determining zero-force members, and explain the importance of finding zero-force members in truss analyses. 7 m Figure 9 A B C D H G F 7 m 7 m 7 m I 150 kN 250 kN 200 kN 7 m E