CEE511 Structural Dynamics Fall Semester 2010-2011
Homework #2
(Due September 27, 2010) Modeling Discrete Parameter Systems - Equations of Motion 1. 2. 3. Chopra Problem 1.12 Chopra Problem 1.19 Derive the equations of motion for the following pendulum sy
CEE511 Structural Dynamics Fall Semester 2010-2011
Homework #3
(Due October 4, 2010) Single Degree of Freedom Systems Free Vibration 1. 2. 3. Chopra Problem 2.6 Chopra Problem 2.20 Consider a heavy mass of weight W on the following beam system:
massless b
GG 454
February 20, 2002
1
RESPONSE OF STRUCTURES (16) Main Topics A Acceleration, velocity and displacement spectra B Resonance and natural frequencies C Response of structures I I Displacement, velocity, and acceleration spectra A Spectra represent para
For a typical span AB: Problem 1.1 (a) MAB=2EIL2A+B-3LMAB Objective: Use the slope deflection method in order to analyze the span frame. Draw the shear and moment diagrams.
Solution Summary: 1) Unknown/known deflections: A,B,C,D= ? ; A, B, C, D=0 2) Fixed
A H M 531
Structures 2: Slope Deflection Method
By: Ahmed Essam Mansour
AHM531 The Civil Engineering Center
The Civil Engineering Center
1
Visit www.AHM531.com for more lecture notes and E-books!
A H M 531
Structures 2: Slope Deflection Method
By: Ahmed E
SHEAR MODULUS The shear modulus is the elastic modulus we use for the deformation which takes place when a force is applied parallel to one face of the object while the opposite face is held fixed by another equal force. When an object like a block of hei
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" 0 " 1 0) 1 " " ")
2" "
3
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4 "* "* " )
M AB
1 = M BA 2
/
4 5 * ) 5 ) 0 * " "
I M BA = 4 E tan L I = 4E (for small values of ) L
/
4 "* 5 ) 5 * 5
I (for small values of ) L
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M BA = 3E
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A H M 531
Structures 2 : Moment Distribution Method
By: Ahmed Essam Mansour
The Civil Engineering Center
1
Visit www.AHM531.com for more lecture notes and E-books!
A H M 531
Structures 2 : Moment Distribution Method
By: Ahmed Essam Mansour
The Civil Engin
The generation of in-elastic response spectra for earthquake acceleration records
Athol J. Carr
University of Canterbury, Christchurch, New Zealand.
ABSTRACT: In 1960 Newmark showed that the displacements of inelastic structures subjected to earthquake ex
UNIVERSITY OF MICHIGAN Official Examination Booklet
Question 1 2 3 4
Score
Total
Name of Student: Date of Examination: Course: October 13, 2010 CEE511 Midterm #1
The University of Michigan Honor Code
The Honor Code outlines standards for ethical conduct f
CEE511 Structural Dynamics Fall Semester 2010-2011
Homework #10
(Due Monday, December 13, 2010) Submit to Prof. Lynchs Mailbox in 2340 GG Brown Multiple Degree of Freedom Systems Spectral Analysis
A lumped mass undamped structural system is shown below:
p
CEE511 Structural Dynamics Fall Semester 2010-2011
Homework #6
(Due November 8, 2010) Numerical Integration and Response Spectra 1. Consider the response of the Ann Arbor water tower to ground motion:
Ann Arbor
w = 386.4 kips
k = 100 kips/in
ug
Not knowin
CEE511 Structural Dynamics Fall Semester 2010-2011
Homework #5
(Due November 1, 2010) Single Degree of Freedom Systems Impulsive Excitations 1. 2. 3. 4. 5. Chopra Problem 3.18 Chopra Problem 3.26 Chopra Problem 4.5 Chopra Problem 4.13 After graduation, yo
CEE511 Structural Dynamics Fall Semester 2010-2011
Homework #4
(Due October 11, 2010) Single Degree of Freedom Systems Harmonic Excitation 1. 2. 3. 4. 5. Chopra Problem 3.1 Chopra Problem 3.3 Chopra Problem 3.5 Chopra Problem 3.7 Chopra Problem 3.11
Problem 2.6
1. Determine deformation and velocity at impact.
u(0)=T£=19-=02 in.
k 50
am) = 1/2gh = ~1/2(386)(36 = ~166.7 in./scc
2. Determine the natural frequency.
a) :fkgz (swam 24393 rad/sec
" w v 10
3. Compute the maximum defamation.
L2(O)
a)
u(t)
CEE511 Structural Dynamics Fall Semester 2010-2011
Homework #1
(Due September 20, 2009) 1 a) b) c) d) e) 2 a) b) c) d) Trigonometry (Assume A and B are constants)
sin( A B ) ? cos( A B ) ?
Show cos Ax sin Bx 0.5(sin[( A B ) x ] sin[( A B ) x ]) Show cos A