Structural Analysis

Figure Q4 shows a beam, loaded at leftmost position A with 30KN, loaded in the middle with 100kN and a final load at the rightmost position E with 30kN. The beam is constructed from two types of plates, as shown in the figure, of lengths Y=2.4m and Z=2.2m. There is a left reaction force of RB at position B and a further right reaction force at RD at position D. Calculate the Bending Moment value (using the convention given to you in the module's formula book) at a position of x=5.3m. State your answer in terms of kilo-Newton-metres to one decimal place. 30 kN A Ym X = ? B Zm 100 kN с Zm Figure Q4 Bending Moment Value? D Ym 30 kN E (5 marks)

A block of metal with a Young's Modulus of E=70GPa and Poisson's ratio of 0.3, has dimensions of 41x20x60 mm for the lengths X, Y and Z respectively as illustrated in Figure Q10. The block experiences a tensile force in the x-direction of 250kN and also an applied tensile force in the z-direction of 50kN as illustrated in Figure Q10. Calculate the change in length experienced in the x-direction in terms of x10³ milli-metres. Stating your answer to the nearest whole number. 250 kN 50 kN X mm Y mm Figure Q10 Z mm X 50 kN 250 kN (5 marks)

Figure Q8 shows a symmetric cross-section of a I-type beam which is constructed from five metal plates each having a width of 12mm and the other sectional lengths are X=64mm, Y=48mm and Z=20, where are the outer flange sections, the inner flange sections and the web section respectively. Calculate the second moment of area in units of mm4, stating your answer to the nearest whole number. X mm Y mm 12 mm Y mm X mm Z mm Figure Q8 12 mm 12 mm 12 mm 12 mm (5 marks)

Part A Given: y = 200 MPa 1. Determine the plastic moment (at zero axial force) 2. Describe how you would obtain the collapse plastic moment given the value of a tensile axial force 3. Sketch the Moment-Axial Force (tensile) interaction diagram and identify at least 5 points on that curve

Part B Given: σy = 200 MPa 1. Determine the plastic moment (same as last problem) 2. Determine the yield moment 3. Determine the plastic shape factor 4. Specify the steps to calculate the moment-curvature relation 5. Calculate, tabulate and plot the moment-curvature relation

Part C Given: y = 200 MPa all members - pefectly plastic (no hardening) Beams-Rectangular cross-sections: height=40cm, width = 20 cm Columns - Square cross-sections: height = 20cm 1. Using ANSYS, simulate the behavior of the frame shown for λ = 1, 1.25, 1.5, 1.75 and 2.0. Document your result by providing snapshots of the moment diagrams for A-1.25. Do all the simulations converge? 2. From the ANSYS results, identify the interval for the collapse load factor (I.E. between what 2 lambdas). 3. From the ANSYS simulations, identify where and in what sequence do the plastic hinges form. 4. Based on the location of the plastic hinges, use manual calculations to estimate the collapse load factor 5. Manually sketch the bending moment diagrams of beam DE at the collapse load

Problem 6: CLO 1 The truss shown is used to support the floor deck. The uniform load on the deck is 2.5 kft. This load is transferred from the deck to the floor beams, which rest on the top joints of the truss. Determine the force in each member of the truss, and state if the members are in tension or compression. Assume all members are pin connected.

Problem 5: CLO 1Determine the force in each member of the trusses shown below.

Use the Moment Distribution Method to analyse the frame when subjected to the loading shown. Dimensions and load values, which depend on your student ID, are given in the table below. Determine the member forces and support reactions required in the table below. Enter your answers in the space provided.

Problem 7: CLO 1 The cable supports the loading shown. Determine the magnitude of the horizontal force P so that x = 6 ft.