View
217
Download
0
Category
Preview:
Citation preview
8/14/2019 SampleProblemsFinalAnswers.epdf
1/6
Name: ______________________________
Continue your work on reverse side
University of Wisconsin Madison; ME 306
Problem Find the reactions , &A A BR M R due to the load P. Assume that the bar has inertia I and
Youngs modulus E. Do you get the expected reactions in the limit 0k . You may use the
information given on the right.
Solution:The deflection at B is:
( ) ( )3 3 3 3
3 3
4.5 36 6
3.5 2
6 6
= +
=
B
B
P RL L L L
EI EI
P L R L
EI EI
3 3
3
3
3 3
3.5 2
6 6
3.53.56
2 6 21
6
=
=
= =+
+
BR k
P L k L
EI EI
P LP LEI
k L EI k L
EI
3
3
3.5
6 2= =
+B
kP LR k
EI k L
From force balance:
( )
3
3
33
3 3
3.5
6 2
1.5 63.56 2 6 2
+ = =+
= =
+ +
A B
A
kP LR P R
EI k L
P k L EIkP LR PEI k L EI k L
From Moment Balance about A
P
8/14/2019 SampleProblemsFinalAnswers.epdf
2/6
Name: ______________________________
Continue your work on reverse side
4
3
4
3
4 4
3
3
3.51.5
6 2
3.51.5
6 2
3.5 1.5 (6 ) 3.5
6 2
1.5 (6 )
6 2
+ = =+
= +
=
+
=
+
A B
A
A
A
kP LM PL R L
EI k L
kP LM PL
EI k L
kP L PL EI kPL
M EI k L
PL EIM
EI k L
In the limit 0k 0=BR ; = AR P; 1.5= AM PL , as expected.
8/14/2019 SampleProblemsFinalAnswers.epdf
3/6
Name: ______________________________
Continue your work on reverse side
8/14/2019 SampleProblemsFinalAnswers.epdf
4/6
Name: ______________________________
Continue your work on reverse side
Problem 4 Determine the maximum height h from which the diver can jump onto the board so
that maximum being stress in the wood does not exceed 6 ksi. The board thickness is 1.5 inch
and its width is 18 inches. Use6
woodE 1.8 * 10 psi= . Assume the diver weighs 180 lbs.
Solution:Using the energy principle, the equivalent load is defined as:0.5 ( ) = +P mg h
We now must determine the relationship between the deflection and load. The reactions forces
are at the left and right are:
1
2
8 / 3
11 / 3
=
=
R P
R P
The moment diagram can be computed as follows.
1
2
( ) 8 / 3;0 3
( ) (11 ) / 3;3 11
=
Recommended