20
Struts
Therefore,
a0
2
kL
v=
Note that
sin
1
x
L
2 2 EI P
cr
=
=
2
kL
L P
P
where
Pcr =
2 EI
L2
Therefore,
v=
a0 sin x
L
=
P cr
1
P
v0
1
Pcr
P
The total deflection
= v + v0 =
L
2
The maximum deflection occurs at x =
max =
P a0
x
x
sin
+ a0 sin
Pcr
1.3 Exercises
21
Table 1.2: Solution to exercise (1.1)
(a)
Radius (r)mm
100
150
150
200
(b)
100
150
200
1.3
r (M P a) (M P a)
-207
+263
-76.4
+132.4
-76.4
+272.9
0
+196.5
207
+345
-53.7
+191.7
0
+138
Exercises
Exercise 1.1. A pressure vessel is to be used
2.3 Exercises
2.3
55
Exercises
Exercise 2.1. Using a double integration approach, calculate all the support
reactions of a propped cantilever, length 12 m, carrying a distributed load
that varies linearly from 20 kN/m at the propped end to 30 kN/m at the
20
Rotating Rings, Discs and Cylinders
1.3
Exercises
Exercise 1.1. A thin disc of inner and outer radii 180 mm and 360 mm
respectively rotates at 160 rad/s. Determine the maximum radial and hoop
stresses. Assume = 0.33 and = 7700 kg/m3 .
Answer. (a) r = 2
24
1.3
CHAPTER 1. DEFLECTION OF BEAMS
Exercises
Exercise 1.1. Fig. 1.19 shows a beam 8 m long and simply supported at its
ends. The beam supports a uniformly distributed load of magnitude 60 kN/m
over a span of 4 m, a center point load of magnitude 160 kN
28
1.3
1.3.1
CHAPTER 1. ENERGY METHODS
Exercises
Strain Energy Methods
Exercise 1.1. A chain link made of a circular section rod has dimensions
as shown in Fig. 1.16. Show that if d, the diameter of the section is assumed
small compared with R, the mean r
SOLID AND STRUCTURAL
MECHANIC 1
Analysis of pin joined frames and
connections, Analysis of Thin Walled
Pressure Vessels
Analysis of pin joined frames
6-3
Introduction
For the equilibrium of structures made of several
connected parts, the internal forces
48
CHAPTER 2. SHEAR FORCE AND BENDING MOMENT
When x = 3, M = 77.5 kN m and when x = 6, M = 92 kN m
6 < x < 10 (See Fig. 2.29(c)
V +
q o x2
+ 24.33 30 50 = 0
2L
or
x2
2
When x = 6, V = 37.67 kN and when x = 10, V = 5.67 kN
V = 55.67
Moment equilibrium;
2
SPRINGS
Exercises
Question one
A close coiled helical spring has mean diameter of 80 mm, a spring constant of 90 kN/m and
has 10 coils. Assuming G= 80 GPa:
(a) Determine a suitable diameter of the spring if the maximum shear stress is not to
exceed 270 MP