CE 332 Exam 1
Name:
Show all of your workl
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Section:
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Problem lao (3 points) Calculate the support reactions for the beam shown below in Figure 1,
Problem Ib.YpointS)
Draw the shear diagram for the beam on the space provided,
Prob
CE 332 Exam 1
Section:
Problem
1 (24 points):
So LVllarJ
Show your work and draw the requested diagrams on the places
provided.
.
lao (8 polntsj-Draw the-Free Body Diagram (FBD) for the beam shown in Figure I .
lb.
(6 points) Draw the Shear Diagram (V) fo
1
CE 332 - Introduction to the Flexibility Method
Please Read and Reference Chapter 10 from the Hibbeler text
Applying the Flexibility
Method to solve Linear Elastic, Statically Indeterminate
Structures
Flexibility Method (A.K.A)
Method of Consistent Defo
I,
CE332 - Deflection of Beams by Virtual Work - Examples
Example 1: Calculate the vertical deflection at B (i.e. OBv) for the following structure. EI is
constant.
5k
2 klft.
RAY
!
RAx-Ef
B
M
A
C
A
4 ft.
E
D
4 ft.
10 ft.
REV
Step 1: Is the structure deter
CE332 Exam #2
Name:_-=S,-,_I_(A_~,-'o-,-i1,-_
Section:
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Closed book, notes and neighbor.
Be sure to show all work, including equations used.
I. Calculate the vertical deflection at D for the following structure. EI is constant f?r all
members.
"
I
0 (\
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CE 332 Exam 2
Be sure to show a IIof your work.
Name
Section
SoLI1ion
_
Problem Ia (25 points): Calculate the horizontal deflection 01" thc roller support A for the frame
shown in Figure I.
Problem tb (3 points):
Sketch the qualitative deflected shape dir
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(E332 Exam 2: Show all of your work - it
Name:
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Section:
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CE332 Exam 1: Show all of your work.
Problem 1. (40 points)
Analyze the following structure in Figure 1. On the spaces provided draw
.
wor
1a. Free Body Diagram (FBD)
lb. Shear Diagram (V)
1c. Moment
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Qualitative Influence Lines and Loading Patterns for an
Indeterminate Frame
problem statement
Using the MUlier Breslau Principle, draw the influence lines for the moment and shear at the
midspan of beam AB, and the moment at B in member Be. Draw the loadi
Influ r '"'
Qualitative Influence Lines and Loading Patterns for
an Multi-span Indeterminate Beam
The MUller Breslau Principle, used previously to draw the influence lines for statically
determinate structures, can also be extended to define the influence
Influence Lines for a Statically Determinate Continuous
Beam
problem statement
Draw the qualitati ve influence lines for the vertical reactions at the supports, the shear and
moments at sections s I and s2, and the shear at the left and right of support B
Influence Lines using the MOiler Breslau Principle
MOiler Breslau Principle
The MUller Breslau Principle is another alternative available to qualitatively develop the
influence lines for different functions. The MUller Breslau Principle states that the
or
CE 332 - Introduction
to Influence Lines (Ch, 6 in Hibbeler)
What is an influence line?
A diagram used when you have movable (i.e. live) loads that shows the effect of
the location of that movable load on a specified:
Reaction
Moment at a given point
Shea
CE 332 ._ Moment Distribution
Moment Distribution
for frames (Part 4)
for Braced Frames
Moment Distribution for braced frames is exactly the same as Moment Distribution for
beams. You will just have to add extra members at some joints.
Example:
8k
2 k/ft.
Step 6: Distribute the UM's based on the OF tor each member
moments as appropriate.
Step 7: Carryover
Note: When looking at a specific joint, that joint is unlocked while all others are locked.
Step 8: Repeat Steps 5, 6. and 7 until unbalanced moments are
CE332 Notes - Moment Distribution,
Example Moment Distribution
Part 3
Problem
Calculate all reactions and draw the V and M diagram for the following problem
0.5 k
B
A
J7
,
~
C
0.8 kif
J
I
I
<
15ft.
20ft.
of Moment
Distribution,
we can say that the above s
Example Moment Distribution Problem
Calculate all reactions and draw the V and M diagram for the following problem
12 k
A
p
B
4 kif
I
1
C
t~
/9/
,
,
,
,
,
20 ft.
7
8 ft.
15 ft.
0
/);)7
,
7
,
8 ft.
Step 1: Set up your Moment Distribution Table
Join
Member
Example 1 Solve using moment distribution, EI is constant.
r
~A
I, 5 ft
,I.
B
C~
l1f1iT
5 ft
.1.
,I
20 ft
1. First, let's set up a table to keep track of things:
Joint
Member
A
AB
C
CB
B
BA
BC
Stiffness,k
DF
FEM
Unbalanced Moments (UM)
Distribute UM's
Car
CE 332 - Introduction
to Moment Distribution
Method
What is Moment Distribution?
An approximate method for analyzing indeterminate beams and frames
One of the most notable advances in structural analysis prior to computer analysis
developed in the 1930s b
Direct Displacement Method
Indeterminate Frame
problem statement
Using the direct displacement method, determine the [mal member end forces in the
indeterminate frame below. The modulus of elasticity (E) and the moment of inertia (1)
are constant for the
Direct Disptecemetv: Method (3)
Three-Span Indeterminate Beam
problem statement
Using the direct displacement method, determine the final member end forces in the
three-span indeterminate beam below. The modulus of elasticity (E) and the moment of
inertia
Direct Displacement Method, Part 2
Example Problem:
Two-Span Indeterminate Beam
problem statement
Using the direct displacement method, determine the final member end forces in the twospan indeterminate beam below. The modulus of elasticity (E) is constan
Direct DlsplacemuJt M thud
Introduction
The direct displacement method is another technique that can be used to analyze
indeterminate structures. This method can be generalized and is commonly used in
structural analysis software.
In this method, all degr
Quiz 2
CE 332
Draw Axial, Shear and Moment diagrams for the frame shown below.
All your calculations
MUST be
organized and clear. Label all values on the diagrams.
12 k
D
C
12
1.5 klft
B -> X~
0
0
A
J-"-6'-7I~:~-'=9L-'. -,cfw_' _
-",9_'
-;>'7r~-C9:L'
-~7r
CE 332 Pre-Course
Fall 2010
Quiz
Name
Sec:
1.
The summation of moments about any point due to all support reactions, support moments, and all applied loads
acti ng on a structure must be O.
(I
2.
True
c
False
The following structure may be classified as (