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

Problem 4: 9-26. Determine the displacement and slope at point C of the cantilever beam. The moment of inertia of each segment is indicated in the figure. Take E=29(10³)ksi. Use the principle of virtual work.s

Problem 5: *9-36. Determine the slope and displacement at point B. Assume the support at A is a pin and C is a roller. Account for the additional strain energy due to shear. Take E=200GPa, I=125x10^6mm, G=80GPa, and assume AB has a cross-sectional area of A=4.5x10³mm². Use the method of virtual work.

Problem 8: 9-57. Determine the slope at A and the vertical displacement at B Use the method of virtual work.

9-49. Determine the vertical displacement of joint D. Use the method of virtual work. Take E=29(10³) ksi. Assume the members are pin connected at their ends.

Problem 6: 9-46. The L-shaped frame is made from two fixed- connected segments. Determine the horizontal displacement of the end C. Use the method of virtual work. El is constant.

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

Question 8. Determine the shear and moment throughout the beam as a function of x.

The figure (not drawn to scale) shows a overhanging metallic bar (supported at A and C), of flexural modulus EI. It is subjected to a point load of amplitude Pat B, and UDL load w between points C and D. All distances are multiple of a unit distance L. You are given the distance between A and B as 4 x L, the distance between B and C as 3 x L, and the distance between C and D as 5 x L (The length of the beam is thus 12 x L.) All answers can be expressed i term f fractions timed by functions of P, w, L and EI. a) Calculate the reaction forces at points A and C, RA and Rc. b) Calculate the binding moment at point C M c) Calculate the slope at point A ₁ d) Calculate the deflections at point D &

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)