h EL = 50 EL = 30

h EL = 50 EL = 30

Calculate the instantaneous deflections and the long term-term deflections after 15 years for the flat roofbeam shown below (simply supported). Use fy = 60,000 psi, fc′ = 4000 psi, and assume that the uniformdead load value shown does not include beam weight, and that none of the concentrated live loads aresustained. The concrete weight is 135 pcf. Investigate the deflection acceptability of the beam accordingto the ACI Code.

a) Determine the global stiffness matrix of the beam shown in Figure below. Assume supports at 1 and 3 are rollers and the support at 2 is a pinned support. Indicate the degrees-of freedom in all the stiffness matrices. EI is constant. Use the values of w and L1 as 50 kN/m and 1.75m, respectively. Note, L2=3L1. b) Determine the rotations at all the nodes of the beam and reactions at the supports. Show all calculations. c) Draw the BMD of the beam on the compression side showing the salient values. What are the maximum bending moments of the beam? Draw the deflected shape of the beam.

20 ft 8 #8 in 2-layers 18 in 30 in

a) Calculate the BMs (bending moments) at all the joints of the beam shown in Figure below using the moment distribution method. The beam is subjected to an UDL of w kN/m. L1= 0.4L. Assume the support at C is pinned, and A and B are roller supports. E = 200 GPa, I = 250x10^6 mm4. Use the values of w and L as 50kN/m and 5m respectively. b) Draw the shear force and bending diagrams for the entire beam. c) Calculate the BMs at all the joints of the same beam shown in Figure using the slope deflection method. d) Compare the values of BMs obtained using the two methods a) and c) and comment.

The interior floor beam shown below at 3-year service life according to the ACI Code, supports partitions,etc. Maximum service load moments are 38 kip-ft dead load and 29 kip-ft live load. Assume that 50% ofthe live load is sustained. Use fc′ = 5000 psi, fy = 75,000 psi.a. Determine if the minimum deflection criteria from ACI is satisfied.b. Find the effective moment of inertia.c. Find the maximum instantaneous and long-term defecations.d. Check if the deflections are within ACI allowable limits

a) For the truss shown in the figure below, determine the stiffness matrices of elements 2, 3 and 4 in the in the global co-ordinate system. Assume for each member A = 0.0015 m2 and E = 200 GPa. Indicate the degrees-of freedom in all the stiffness matrices. b) Determine the stiffness matrix of the whole truss in the global co-ordinate system. Clearly indicate the degrees-of freedom numbers in the stiffness matrix. c) Calculate all the nodal displacements and all the member forces of the truss.

a) Draw a 2D element and show the dofs (degrees of freedom). Draw all the 2D elements used in Strand7. Explain the differences between these elements in terms of the no. of nodes and interpolation/shape functions used. b) A 8 m x 8 m plate (in the xy plane) with 8 mm thickness, is fixed at all the edges and is loaded by a pressure loading of 4 kN/m2 in the downward (-z) direction. The plate is made of steel (E = 200 GPa, density = 7850 kg/m3). Explain the steps involved in setting up a Strand7 model for this problem. Your explanation should include how the given input data for this problem will be used in Strand7 modelling. Explain how you would determine the maximum deflection from the Strand7 output.