Consider the truss framework shown in figure Q2 below. The trusses are constructed from a steel alloy with E = 200 GPa. The lengths and orientations of the trusses are shown in the figure. You may assume that the truss labelled "E3" is orientated at 90° to the positive x-axis. The central point in the framework supports a vertical load of 100kN and a horizontal load of 50kN as shown. The remaining points in the framework are fixed to immovable walls. You are required to carry out a finite element analysis to determine the displacement of the central point of the framework due to the applied loads. L1 = 50m L2 = 50m L3 = 50m E3 50 kN E1 100 kN E2 ? = 53° ? = 127° Figure Q2 Q 2(a) [15 Marks] Given a cross sectional area of all trusses = 5 x 10-4m², determine the stiffness matrix for each of the three trusses E1, E2 and E3. Q 2(b) [10 Marks] Using your result from part (a), construct the global stiffness matrix for the truss framework. Q 2(c) [15 Marks] Using your result from part(b), construct the global problem equation and hence solve for the displacement of the central point. Comment on your answer – do the displacements seem logical? Q 2(d) [10 Marks] Using your results from part (c), determine the stress in the truss E1.
Added by Amber W.
Close
Step 1
For truss E1, E2, and E3, the stiffness matrix would be: k_E1 = (200 GPa * 5 x 10^-6 m^2) / 50 m = 20 kN/m k_E2 = (200 GPa * 5 x 10^-6 m^2) / 50 m = 20 kN/m k_E3 = (200 GPa * 5 x 10^-6 m^2) / 50 m = 20 kN/m Show more…
Show all steps
Your feedback will help us improve your experience
Supreeta N and 92 other Physics 101 Mechanics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
1. Column design charts are provided for this question. Figure Q.1 shows a reinforced concrete braced building frame to be cast from concrete having cylindrical compressive strength of fck = 25 N/mm² and reinforced with reinforcing bars having yield strength of fyk = 460 N/mm². The frame consists of rectangular beams (300 mm width, 500 mm height) and square columns (420 mm x 420 mm). Concrete cover to the centroid of all main reinforcements is to be 30 mm. If the load arrangement as shown in Figure Q.1 yields an ultimate axial load F = 2000kN (in the direction of column) at point A, and ultimate bending moments M = 160kN at both points A & B (giving tension on same sides of column AB): (a) Determine the slenderness ratio of column AB. Further suggest whether the column should be considered as "short" or "slender" in the column analysis. (Ans: Slender column) [15 marks] (b) Determine the required area of reinforcement for column AB. The effective creep ratio can be assumed to be φef = 0, and Young's Modulus of the reinforcing bars to be Es=200 kN/mm². (Ans: As = 1917 mm²) [20 marks]
Adi S.
Learning Goal: To apply the method of sections to find the forces in specific members of a truss. The method of sections is used to find the force in a specific member of a truss and is based on the principle that, if a body is in equilibrium, then every part of that body is also in equilibrium. When applied, the method of sections "cuts" or sections the members of a truss and exposes their internal forces. To find the unknown internal member forces, the free-body diagram of a section is drawn and the equations of equilibrium are applied: Σ Fx = 0 Σ Fy = 0 Σ Mo = 0 Because there are only three independent equilibrium equations, section cuts should be made such that there are not more than three members that have unknown forces. Part A As shown, a truss is loaded by the forces P1 = 510 lb and P2 = 202 lb and has the dimension a = 9.70 ft . Determine FBC , the magnitude of the force in member BC, using the method of sections. Assume for your calculations that each member is in tension, and include in your response the sign of each force that you obtain by applying this assumption. Express your answer numerically in pounds to three significant figures.
Sri K.
Question (50pts.): For the truss and loading given below: a) Draw the free-body diagram of the truss. (5 pts.) b) Calculate the support reactions at supports A and B. (3 x 4 pts.) c) Determine the magnitude and direction of the internal forces in truss members. • Analyze joint A. Find the magnitude and direction of the internal forces in members AD and AC. (2 x 4 pts.) • Analyze joint B. Find the magnitude and direction of the internal forces in members BC and BE. (2 x 4 pts.) • Analyze joint D. Find the magnitude and direction of the internal forces in members DE and DC. (2 x 4 pts.) • Analyze joint E. Find the magnitude and direction of the internal force in member EC. (4 pts.) d) Draw a diagram of the truss. Write the magnitude and direction of the internal forces in truss members on the diagram as shown in lecture notes. (5 pts.) 12kN 7 kN D E 13m A 60º 60º B 15m C 15m
Manish J.
Recommended Textbooks
University Physics with Modern Physics
Physics: Principles with Applications
Fundamentals of Physics
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD