MEC2025F Mechanics of Solids
Tutorial 10: Bending Stresses
6 June 2017
See the recommended reading list in the course outline for the sources of the problems.
1
Bending Stress
1. A sawmill cuts rectangular timber beams from
circular logs. If two beams of
MEC2023F - Dynamics I - Class Test 2
Department of Mechanical Engineering
University of Cape Town
Question 1 [10 marks]
The disk of radius r is confined to roll without
slipping at A and B. If the plates have the
velocities shown, determine the angular ve
MEC2025F Mechanics of Solids
Tutorial 7
16 May 2017
See the recommended reading list in course outline for the sources of the problems.
1
Shear Force and Bending Moment Diagrams
For all structures that follow determine the support reactions and draw the c
MEC2025F Mechanics of Solids
Tutorial 8: Bending
23 May 2017
See the recommended reading list in the course outline for the sources of the problems.
1
Shear Force and Bending Moments
For all structures that follow unless otherwise indicated determine the
MEC2023F - Dynamics I - Class Test 1
Department of Mechanical Engineering
University of Cape Town
Question 1 [6 marks]
The train engine at E has a speed of 22 m/s and an
acceleration of 10 m/s2 acting in the direction shown. Find
the rate of increase in t
MEC2023F Dynamics I Class Test 3
Department of Mechanical Engineering
University of Cape Town
2016
Time: 90 mins
Marks: 50
Instructions:
This is a closed book test
A formula sheet is provided
Answer all questions
Questions may be attempted in any orde
MEC2025F Mechanics of Solids
Tutorial 9: Bending Stress
30 May 2017
1
Stress Transformations
p1 = 148.8
1. y = 145 MPa
xy = 21.84 MPa
p2 = 3.2
max = 76.0 MPa
2
Bending Stress
2. max =
Eh
2r + h
(a) Left of B max = 11.9 MPa
(b) Right of B Mb = 6 106 N.mm,
MEC2025F Mechanics of Solids
Tutorial 10: Bending Stress Solutions
6 June 2017
1
Bending Stress
1. Use calculus to maximise the either use
pythagoras or use trigonometric angles to
solve for one variable.
3d
6d
b=
,h=
6
3
L
d
= 0 at x =
dx
4
max
x=
=2
B
6
7. Bending Stress
Tree blown over by strong wind. A knowledge of where the maximum bending stress will occurs
give us an idea of why trees when blown over come off by the root and dont snap at the trunk.
7.1 Introduction
In the previous chapter we saw how
MEC2025F Mechanics of Solids
Tutorial 9: Bending Stresses
30 May 2017
See the recommended reading list in the course outline for the sources of the problems.
1
Stress Transformations
1. A road sign is supported by a pipe (see figure) having outer diameter
MEC2025F Mechanics of Solids
Tutorial 10: Bending Stresses
6 June 2017
See the recommended reading list in the course outline for the sources of the problems.
1
Bending Stress
1. A sawmill cuts rectangular timber beams from
circular logs. If two beams of
MEC2025F Mechanics of Solids
Tutorial 9: Bending Stress
30 May 2017
1
Stress Transformations
p1 = 148.8
1. y = 145 MPa
xy = 21.84 MPa
p2 = 3.2
max = 76.0 MPa
2
Bending Stress
2. max =
Eh
2r + h
(a) Left of B max = 11.9 MPa
(b) Right of B Mb = 6 106 N.mm,
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
2017
Tutorial 1
The speed is the slope of the curve, so answer c) is true. The acceleration is the second derivative of
the position. Since As position increases linearly the
MEC2025F Mechanics of Solids
Tutorial 3: Stress Transformations
4 April 2017
See the recommended reading list in course outline for the sources of the problems.
1
Stress Transformations
1. At a cross-section of a beam when there is a longitudinal stress o
MEC2025F Mechanics of Solids
Tutorial 4
11 April 2017
See the recommended reading list in course outline for the sources of the problems.
1
Stress Transformations
1. Consider a bar under pure axial loading, what
is the angle of maximum shear? If the tensi
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
2017
Tutorial 3
1. The rod AB rotates abouth the z-axis with the constant angular speed
4.00 rad/s while the slider A moves up the rod at the constant speed of
1.00 m/s. Dete
MEC2025F Mechanics of Solids
Tutorial 1 Solutions 2017
Review of Statics
See the recommended reading list in course outline for the sources of the problems.
1
Review of Statics
1. Determine the magnitude of the resultant
force and its direction measured c
MEC2025F Mechanics of Solids
Tutorial 3: Stress Transformations
Solutions
See the recommended reading list in course outline for the sources of the problems.
1
Stress Transformations
1. n = 19.06 MPa
nt = 15.32 MPa with the t-axis defined positive
from to
MEC2025F Mechanics of Solids
Tutorial 4 Solutions
11 April 2017
See the recommended reading list in course outline for the sources of the problems.
1
Stress Transformations
1. = 45
Normal stress =
x
2
Maximum shear stress =
x
2
3. = 12 MPa , = 16 MPa shea
MEC2025F Mechanics of Solids
Tutorial 1 2017
Review of Statics
See the recommended reading list in the Course Outline for the sources of the problems.
1
Review of Statics
1. Determine the magnitude of the resultant
force and its direction measured counter
MEC2025F Mechanics of Solids
Tutorial 2 2017
Solutions
See the recommended reading list in course outline for the sources of the problems.
1
Truss Analysis
1. FAy = 2.250 kN
Ay =
FEF = 1.688 kN
Cy = 3.0 kN,
FBE = 0.4507 kN
FBC =
(b) F1 = 1.697 kN
2.063 kN
2016/04/28
Work and Kinetic Energy
MEC2023F
MEC2023F
It was noted in the previous lecture that the work-energy
equation for rigid bodies has three cases:
Rigid bodies: Power,
Efficiency &
Potential Energy
Lecture 36
(a) For rigid body translation:
= 12 2
MEC2023F
Surname
Tutorial Test 6
Name
Student Number
The velocity vector diagram of the slotted mechanism
for the instant shown is given (to scale). Bar AB has an
angular acceleration of 10 rad/s2 (CW). Draw the
acceleration vector diagram in the space pr
2016/04/08
General Equations of Motion
MEC2023F
Plane Kinetics of
Rigid Bodies
Translation
For planar motion of rigid bodies, Newtons second law of
motion can be written as
= =
where and is the resultant unbalanced force acting on the
particle, and is
2016/04/28
Work and Kinetic Energy
MEC2023F
For particles, the work-energy equation was derived:
MEC2023F
1 + 12 = 2
where:
Rigid bodies: Work
and Kinetic Energy
12 represents the total work done by all forces acting on the
particle as it moves from state
UNIVERSITY OF CAPE TOWN
DEPARTMENT OF MECHANICAL ENGINEERING
MEC2023F Dynamics I
1. A car drives down a spiral ramp that has a constant
radius and constant rate of descent as shown. If the
car drives at a constant speed of = 1.5 m/s,
determine the magnitu