题目
2025 SP 14:440:221 ENG MECH-STATICS (05 - 08) Lecture 13
单项选择题
When using the Method of Joint for force analysis of a truss structure, how many equations of equilibrium are available at each joint?
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标准答案
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思路分析
When applying the Method of Joint for a 2D truss, each joint is analyzed by ensuring equilibrium in both horizontal and vertical directions.
At any given joint, the forces acting along the connected members and any external loads must balance such that:
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类似问题
For the truss shown, determine by inspection whether the forces in AB, AC, BC, BD and BE are tensile, compressive or zero. The force in member AB is Blank 1 Question 5[select: , zero, compressive, tensile] The force in member AC is Blank 2 Question 5[select: , zero, compressive, tensile] The force in member BC is Blank 3 Question 5[select: , zero, compressive, tensile] The force in member BD is Blank 4 Question 5[select: , zero, compressive, tensile] The force in member BE is Blank 5 Question 5[select: , zero, compressive, tensile]
For the truss shown, calculate the force in member BD if P = 1097 N, a = 3.6 m, b = 2.1 m. Your answer should be positive for tension and negative for compression. Give your answer to two decimal places. Note: consider using method of sections.
A truss is subject to a point load P=849 N. Calculate the force in member BC (tension positive). Note: consider using method of sections.
Question text 13Marks PROBLEM 3 Consider the truss shown below in Figure P3a. It is loaded with seven external forces, labelled [math: F1] F_1 to [math: F7] F_7 , acting at the nodes of the truss. The forces are all positive non-zero forces acting in the directions shown. Figure P3a. Truss with applied forces. (a) How many zero force members are there for this truss loading condition? (1 mark) Answer 1[input] zero-force members (b) Consider the same truss in Figure P3a (above). Select the best classification of its stability and determinacy by selecting from the options below. (1 mark) Answer 2[select: , Stable but statically indeterminate, Unstable and statically determinate, Stable and statically determinate, Unstable and statically indeterminate, Overconstrained but unstable] (c) Now consider the truss shown below in Figure P3b. It is loaded with four external forces, labelled [math: Q1] Q_1 to [math: Q4] Q_4 , acting at the nodes of the truss as shown. Determine the reaction forces [math: Hx] H_x and [math: Hy] H_y at the pin support at Node H, and the vertical reaction [math: Oy] O_y at the horizontal roller support, Node O. Note: all reactions are positive in the direction of x and y axes, respectively, and a counterclockwise moment is considered positive. (5 marks) [math: d=10m] d = 10 \, \text{m} [math: h=15m] h = 15 \, \text{m} [math: θ=40∘] \theta = 40^\circ [math: Q1=200kN] Q_1 = 200 \, \text{kN} [math: Q2=Q3=115kN] Q_2 = Q_3 = 115 \, \text{kN} [math: Q4=200kN] Q_4 = 200 \, \text{kN} Figure P3b. Truss with applied forces. Horizontal reaction at H ([math: Hx] H_x ) = Answer 3[input] kN Vertical reaction at H ([math: Hy] H_y ) = Answer 4[input] kN Vertical reaction at O ([math: Oy] O_y ) = Answer 5[input] kN (d) Now consider the same truss with different forces applied as shown in Figure P3c and listed below. Force [math: P4]P_4 is applied at Node E in the direction parallel with member EL, as shown in the figure. All other external forces are applied vertical (downwards) at the nodes. The reaction forces at the pin joint at H and the horizontal roller at O are provided to you for this loading configuration. (6 marks) Figure P3c. Truss with applied forces. [math: d=10m] d = 10 \, \text{m} [math: h=15m] h = 15 \, \text{m} [math: Hx=50kN] H_x = 50 \, \text{kN} [math: Hy=405.36kN] H_y = 405.36 \, \text{kN} [math: Oy=294.64kN] O_y = 294.64 \, \text{kN} [math: P1=P5=P6=P7=75kN] P_1 = P_5 = P_6 = P_7 = 75 \, \text{kN} [math: P2=P3=135kN] P_2 = P_3 = 135 \, \text{kN} [math: P4=158.11kN] P_4 = 158.11 \, \text{kN} Determine the forces in members DE, LE and LM. Force in member ([math: DE] ) = Answer 6[input] kN (2 marks) Force in member ([math: LE] ) = Answer 7[input] kN (2 marks) Force in member ([math: LM] ) = Answer 8[input] kN (2 marks) Notes Report question issue Question 3 Notes
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