King Fahd University of Petroleum & Minerals

CIVIL ENGINEERING DEPARTMENT

CE 511

First Major Exam

First Semester 2004-2005 (041)

Student Name: _______________________________

Student I.D.: _______________

Grade: ____________

Instructor: Dr. Ahmad S. Al-Gahtani

Problem 1: (20 points)

a) Derive the flexibility matrix corresponding to the coordinates 1 and 2 for the shown cantilever beam AB.

b) Use the flexibility relations [f] {F} = {D} to derive the corresponding stiffness matrix coefficients, .

c) What is the relationship between [f] and [s]?

Problem 2: (40 points)

a) Derive the flexibility matrix for the shown beam corresponding to the redundant forces Q₁ & Q₂ (Fig. 1a).

b) Using the flexibility matrix derived in (a), determine the spring constant if D_spring = D₁/2 where D₁ is the deflection at 1 of the determinate beam under the shown load (Fig. 1b).

Problem 3: (40 points)

a) Write the stiffness matrix corresponding to the coordinates 1 and 2 of the shown frame.

b) Determine the displacements D₁ and D₂ due to distributed load W applied on the beam BC.

c) Determine the displacements D₁ and D₂ if the support E settles vertically by D. (no load W in this case).

d) Determine the moment on the beam BC due to the combined effects at (b) and (c).