Structural Analysis

Q2 The portal frame carries vertical and horizontal forces as shown in the figure below. If Mp is equal to 40 kNm determine the upper and the lower load factors against collapse. Consider at least 2 combined mechanisms. 2 m 60 KN 2 m B E 2M₂ A 2 m 30 kN/m Mp 2 m с Mp D 2 m

Q2: Determine the vertical displacement of joint 6 of the steel truss, shown in Figure 2, using Work-Energy principles and imaginary unit load. The cross- section area of each member is A= 200mm² and E=200GPa. Not: (a) Determine all required internal actions in the members using the pin- joint method or the method of sections C (b) You can use an Excel spreadsheet to calculate deflection once member forces are calculated. (c) Compare the deflection with Multiframe

Q1: Determine all reaction components of the beam shown in Figures 1, using the Force Method Draw the Shear and Bending Moment diagrams

Q1: The beam in Figure 1 is subjected to a concentrated load of 10kN and UDL w=2kN/m. Determine the displacement at point C using Macaulay's method (the double integration method). Take E=200GPa, l=5x106mm4

Q1: The crane travels along a runway girder that is supported on columns at B, C and E as shown in Figure 1. Draw the Influence Lines with the main values for: a) vertical reaction at D b) shear at C c) moment at E; you may use Multiframe to assess the main values

Find the general solution of the forced Mass-Spring system with the following parameters undergoing forcing function F(t). m=3.2kg, k=33N/m, F(T)

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

Question 6. Determine the shear and moment in the beam as a function of x.

Problem #3: GIVEN: A proposed 12 ft tall commercial building that is 160ft long and 70 ft wide, and is situated in Albany, OR

A square cross-section XXX mm beam, 2 metres long, is loaded from above in the middle with a load of Y=2 kN causing a compressive Bending Stress at the top of the beam. The beam i addition experiences a tensile end loading of Z=283 kN causing an End-Loading Stress, as illustrated in Figure Q9. Calculate the width and height of the beam to the nearest millimetre in order to reduce total stress at the top of beam to be near zero? Stating your answer to the nearest millimetre. X mm Z KN Load causing a compressive ing stress bending Y Y KN X mm, Square cross section Z Load causing end-loading tensile stress Figure Q9 Z KN I (5 marks)