Name:
Session:
2
Beam AB and CD (both have constant bending rigidity EI) are connected by the cable BC
(axial rigidity EA, length H). Beam CD is subjected to a uniformly distributed load q as
shown in the figure. Find the internal force of the cable.
A
B
Name:
Session:
For the beam shown below, determine the deflection C in terms of P, L, E and I using
superposition and the tables provided on the next page.
A
B
C
2
Name:
Session:
2
1. Derive the equation of the deflection curve for a beam (EI = constant) subjected to
uniformly distributed load (see figure). Also, determine the deflection at the midpoint of
48 EI
the beam. Assume that the spring constant is k = 3 .
L
Name:
Session:
The cantilever beam is subjected to the loading shown. Draw the shear-force and
bending-moment diagrams and then determine the maximum bending stress. Draw the
freebody diagram first.
Mo
a
V
M
2
Name:
Session:
2
The cantilever beam is subje
Name:
Session:
2
1. Draw the FBD and then find the reactions for the beam shown below.
P
F
M
x
a
Ax
F
y
Ay
a
a
a
=0
A
Ax = P
= 0 3RD a = Pa
RD = P 3
=0
Ay = P 3
RD
2. Draw the shear-force and bending-moment diagrams for the beam shown below,
labeling al
Name: SDWTWIJ Session:
The pressurized tank (E, V) with diameter of 1000 nun is made of 8 mm thick plate. The
normal stress cry (stress in the y-direction normal to the weld) is 60 MPa.
Determine the internal pressure using Mohrs circle. Also determine
1.
A(, 0)
B(3, 0)
x1y1
2.
x = , y =z = 0
1
x ( y + z ) =
E
E
1
y = y ( z + x ) =
E
E
1
z = z ( x + y ) =
E
E
[
]
[
]
[
x =
]
Change in length in x direction: a x =
E
Change in length in y direction: a y =
Change in length in z direction: t z =
a
E
A solid circular bar is fixed between rigid wall at points A and C. A uniformly
distributed torque t is then applied to the bar over the region AB (see figure). Assume
that the bar has shear modulus G and diameter d. Find:
(a) The reaction torques at two
Name:_
Session:_
Problem 1: A stepped shaft ACB is held against rotation at ends A and B and subjected to
a torque T0 acting at section C. The two segments of the shaft (AC and CB) have
diameters dA and dB, respectively, and polar moments of inertia IPA a
Name:
Session:
2
A nonprismatic bar ABC made up of segments AB (length 2L, cross-sectional area 2A)
and BC (length L, cross-sectional A) is fixed at end A and free at end C (see figure). The
modulus of elasticity and the coefficient of thermal expansion o
1
2 nd
2
E M 319
M IDTERM EXAM
3
T ot.
NAME:
SESSION:
April 18, 2008, 4-6 pm, BUR 106
Closed books and notes exam Formula sheet provided
Exercise 1 (20 points)
A cylindrical pressure vessel of radius R and thickness t carries an internal
pressure p and, i
Name:
Session:
2
A bar AB is supported by a hinge at point A and connected to a cable at point B as shown
below. A force P = 140 N is applied at point D that is 300 mm away from point A (see
figure). Given that the cross sectional area for the bar AB is 2
EM 319
1St MIDTERM EXAM
NAME:
SESSION:
October 9, 2007, 6:30-8:30pm, FAC 21
Closed books and notes exam Exercise 1 (30 gointsl
The piie ABC of length L is partially buried in the soil. Assuming that the friction
provided by the soil per unit le
Exercise 3 (40 points)
During the construction of a bridge pier, a solid circular pile is driven into the earth by a
torque To. A distributed torque is induced during this process. The distributed torque
varies linearly in intensity from zero at end D to
THE UNIVERSITY OF TEXAS AT AUSTIN
Department of Aerospace Engineering and Engineering Mechanics
EM 319 MECHANICS OF SOLIDS
FALL 2008
SYLLABUS
Unique Numbers:
14120, 14125, 14130, 14135
Instructor:
Yannis Korkolis, WRW 109, 471-1077, [email protected]
Shear force and Moment diagrams
Procedures for solving a question:
1.
2.
3.
4.
Solve for reactions. (After that, reactions can be regarded as applied forces.)
Draw shear force diagram.
Draw bending moment diagram.
Approaches to draw diagrams: FBDs + equat