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)

An I beam with a symmetric cross-section shown in Figure Q6 has lower and upper sections 2X mm wide and a middle section of X=67mm wide, the top and bottom section depths are lengths of Y=28mm in height, with the middle section depth of 50mm as illustrated in Figur Q6. The beam is pulled apart by a force of 24kN. The length of the beam is Z=22mm long. What is the maximum stress experienced in the shaft in terms of mega-Pascals. State your answer to 1 decimal place. Y mm F = 24 KN Ymm 50 mm ← X mm Figure Q6 2 mm = 24 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

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

Classify each of the following trusses as stable, unstable, statically determinate, or statically indeterminate. If indeterminate state its degree. Indicate the degree of indeterminacy.

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

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.