King Fahd University of Petroleum & Minerals

# CIVIL ENGINEERING DEPARTMENT

## CE 511

First Major Exam

First Semester 2004-2005 (041)

Student Name: _______________________________

Student I.D.: _______________

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    Dspring = 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).