Use the Slope-Deflection equations to determine values of unknown displacements (in terms of E/). Determine moments at A, B, C, D and H and draw the BMD for the frame. Assume that flexural rigidity, El, of member BC is three times of that of members AB and CD.

SOLVE USING METHOD OF LEAST WORK (Castigliano's second theorem)

Consider the frame shown below: (a) Without conducting any analyses, which of the two columns, AB and CD, is expected to experience a larger shear force? Explain the reasons, (b) Using the slope-deflection equations, determine the end moments of all members, (c) Compute the horizontal reactions at points A and D and compare the result with the expectation from part (a). EI is constant and all members are axially rigid. 10 kips B 15 ft A 10 ft с 10 ft D

A tapered bar AB of solid circular cross section and length L is supported at end B and subjected to a tensile load P at the free end A. The diameters of the bar at ends A and B are dA and de, respectively. Determine the elongation of the bar due to the load P, assuming that the angle of taper is small P da A B T dв 1 m