C.E. 321

C.E. 321- W 96

Mid Term Exam 2

Feb. 26 - Mar. 1, 1996

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Name Score

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Time Begin Time End Location

This exam is open book (your textbook only) and open notes, however it must be an individual effort, no help can be sought or used from anyone else.

1. Moment Area Method (25 points) - Find the deflection of the variable-section beam shown below under the concentrated load P. The moment of inertia of the left three-quarters of the span is 2I, while the value for the right one-quarter is I. Find the value of the deflection first in general terms (i.e. as a function of P,L,E and I), and second for the specific values of P= 2 kips, L=40 ft, E=29,000 ksi, and I = 200 in4.

2I I

L/2 L/4 L/4

2. Conjugate-Beam (25 points). Determine the slope and deflection under the concentrated load for the structure shown. Note first 1/4 of beam has 4EI, remainder of beam has EI. Beam fixed at left end, simply supported at right end, internal hinge as shown.

60 kip

4EI EI

(hinge)

10 ft 10 ft 20 ft

E = 30,000 ksi, I = 1,000 in 4

3. Virtual Work (25 Points) Determine the horizontal and vertical components of the displacement at joint c of the pin jointed truss shown below. All members have a cross-sectional area of 0.0025 m2 and a modulus of elasticity of 200 (10) 9 Pa.

225 kN 3 m

` 3 m

a d

4 m 4 m 150 kN

4. Castigliano's Theorem (25 points) Find, by Castigliano's theorem, the horizontal displacement and the rotation at the support c for the frame shown below. Assume constant E and I for both horizontal and vertical members

a b