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FAKULTI KEJURUTERAAN MEKANIKALUNIVERSITI TEKNIKAL MALAYSIA MELAKA
TUTORIAL 3SOLID MECHANICS 2 (BMCS 2333)
SEMESTER 1 SESSI 2007/2008Stress-Strain Energy & Castigliano’s Theorem - Solution
1. Using P, L, E and I, determine the strain energy due to bending for the beam and loading shown in Figure 1. Ignore the effect due to shear stress.
()
SolutionCD portion:
BC portion:
AB portion:
2. The aluminum rod AB (G=26 GPa) is bonded to the brass rod BD (G=39 GPa) shown in Figure 2. Knowing that portion CD of the brass rod is hollow and has an inner diameter of 40 mm, determine the total strain energy of the two rods.
()
Solution,
AB portion:
BC portion:
CD portion:
3. A simply supported beam, AB shown in Figure 3 is subjected to a concentrated load, F at midspan and an uniform distributed load, w N/m. Determine the expression for the elastic strain energy, U due to bending in term of flextural rigidity EI, length L, concentrated load F and uniform distributed load, w.
()
Solution
Figure 1
Figure 3
A BC
D
250mm375mm
400mm
36mm
60mm
Figure 2
TA= 800 Nm
AB
3L
CD
LL
P P
1x1xM
2x2xM
3x3xM
A B
L
w N/mF
x
xM
4. A pin-joined system of three bars, each having the same cross section A, is loaded as shown in the Figure 4. Determine and of joint B due to applied force P.
()
Solution, ..(1)
, …(2)Solve both equations,
, ,
,
,
5. A planar bent bar of constant EI has the dimensions shown in the Figure 5. Determine and , at the tip due to the application of force P.
()
SolutionPortion 1; ,
,
Portion 2; ,
,
Portion 3; ,
,
Figure 4
Figure 5
60
30 PL
A
B
C
Q
3x3xM
1x1xM
a a a
a/2
a/2
P
5x5xM
2x2xM
4x4xM
Q
M
FAKULTI KEJURUTERAAN MEKANIKALUNIVERSITI TEKNIKAL MALAYSIA MELAKA
TUTORIAL 3SOLID MECHANICS 2 (BMCS 2333)
SEMESTER 1 SESSI 2007/2008Stress-Strain Energy & Castigliano’s Theorem - Solution
Portion 4; ,
,
Portion 5; ,
,
6. For the prismatic beam shown in Figure 6, determine deflection at point D.
()
Solution
,
,
Portion EB;
,
Portion DE;
Portion AD;
Figure 6
A B
2L
w
2L
2L
D E
Q
1x1xM2x
2xM3x
3xM
M
