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, ikorko@mail.utexas.edu
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
Review 2
Fall 08
1. A pressurized steel tank is constructed with a helical weld that makes an angle = 60o
with the longitudinal axis (see figure). The tank has radius r and wall thickness t and is
subjected to an internal pressure p. An electrical resista
Review 2
Fall 08
1. A pressurized steel tank is constructed with a helical weld that makes an angle = 60o
with the longitudinal axis (see figure). The tank has radius r and wall thickness t and is
subjected to an internal pressure p. An electrical resista
Review 1
Fall 08
1. A solid circular bar is fixed against rotation at the ends and loaded by a distributed
torque t(x) that varies linearly in intensity from zero at end A to to at end B (see
figure). Assume that the bar has shear modulus G and diameter d
Review 2
Fall 08
1. A pressurized steel tank is constructed with a helical weld that makes an angle = 60o
with the longitudinal axis (see figure). The tank has radius r and wall thickness t and is
subjected to an internal pressure p. An electrical resista
Review 2
Fall 08
1. A pressurized steel tank is constructed with a helical weld that makes an angle = 60o
with the longitudinal axis (see figure). The tank has radius r and wall thickness t and is
subjected to an internal pressure p. An electrical resista
An example of Mohrs Circle
Given a stress state as shown in the figure, construct its Mohrs circle and finish the following:
S2
6000
A
5000
30000
30000
A
R
C
P2
P1
E
6000
x1
B
B
Note: All units are in psi.
x1 y1
S1
Construct the Mohrs circle:
Read coord
Axial Tension and Torsion
=
=
P
A
, =
L
lateral
=
axial
= E
P
x
=
0
P( x)
dx(+ TL )
EA( x)
If P, A are constant: =
PL
(+TL)
EA
Tr
J
r
=
= r
L
= G
E
G=
2 (1 + )
=
T
=
x
0
T (x)
dx
GJ ( x )
TL
r 4 d 4
, J=
=
GJ
2
32
4
4
4
4
(ro ri ) (d o di )
(hollow c
Midterm #2 Formula sheet
Beam bending: Shear forces and bending moments normal and shear stresses
Shown are the positive moments and shears:
q(x)
M(x)
( +)
dV ( x)
= q( x)
dx
dM ( x)
= V ( x)
dx
V(x)
Neutral axis at y , where : y A i = y i Ai
My
bh 3
d 4
Cylindrical pressure vessel
A pressurized steel tank is constructed with a helical weld that makes an angle = 55 with the
longitudinal axis (see figure). The tank has radius r = 1.8 m, thickness t = 20 mm, and internal
pressure p = 800 kPa. The steel has
(all assignments are from the textbook, unless specified otherwise)
1st assignment week of Sept.1st
Read sections 1.1-1.5, examples 1.1-1.3 and exercises 1.2-2,-3,-7,10, 1.3-3,-6 (use software e.g. Excel), 1.4-1,-3, 1.5-1,-3
2nd assignment week of Sept.8t
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