ME-315 Stress Analysis
STRESS CONCENTRATIONS 2
Solution of homework problem 2 on design of a plate with/out a hole
Given two choices of plate material:
(a)
The thickness of the plate if the hole is not present:
The stress induced by the force F:
o
F
F 10
ME-315-001
Stress Analysis:
Fall 2015
Prof. K.A. Narh
Solution of Homework Assignment on Failure Theories (H7)
The uniaxial yield stress for a material is yp =185 MPa. Determine using first the Tresca criterion and
then the von Mises criterion, whether or
Prof. K.A. Narh
ME-315-002: Spring 2015
Solution of Problems on Stress Concentration 1
(1)
45000 psi
(a)
Stress at section AB:
(i)
AB
P
3540
7867 psi
AAB 3 0.15
AB 7867 psi is below proportional limit,
P 45, 000 psi, therefore, the stress BC is in e
Solution for Homework on Stress Function (H4)
1.
Given: Rectangular box abt,
a=6 m, b=4 m, t=112 mm=0.112 m
( x, y) 12 x3 y
2
2
2
36 x 2
a) x 2 0, y 2 72 xy, xy
y
x
xy
(b) Stress element
y=72xy
y
xy=-36x2
x=0
xy=-36*36
=-1296 Pa
xy=0
x
y=0
xy=-36x
2
Homework 3 Problem on Strains (H3)
A rectangular plate (Fig. 1) is acted on by a stress distribution resulting in the uniform strains:
x 300 106 , y 500 106 , xy 200 106 .
(i)
(ii)
Write down the strain tensor.
Write down the strain transformation Equati
ME-315-001
Stress Analysis:
Exam #1
Sample Problems
Prof. K.A. Narh
Note: If a particular topic covered in class is not found in the sample problems, then it is covered in the
Textbook Homework Problems listed in the course schedule. See last page.
1. A b
Home Problem 1: From Lecture 1 Notes (slide 46)
(c) Determine the maximum shear stress (max) and its orientation. (d) Show the results of (b) and (c) on
properly oriented elements. Note: we did part (b) as part of lecture example (slide 46), so dont repea
Prof. K.A. Narh
ME-315: Fall 2015
Solution to Extra Credit Problem on Strains (0.25 pt.)
10 MPa
y
D
20 MPa
5 MPa
C
45 mm
y
45 mm
x
45
A
5 MPa
DB 0.045 2 m
20 MPa
45 + 90
B
x
10 MPa
(a) Normal strains in (i) AB (y) and (ii) BC (x) are obtain using Hookes L
Prof. K.A. Narh
ME-315-001: Fall 2015
Solution for EC Problem on Stress Concentrations
The sketch on the left can be represented by the superposition of two similar sketches as shown
in Fig (b) below:
r1
o a 2
a4
a2
1 2 1 3 4 4 2 cos 2
2 r
r
r
1
Lecture 1
Fundamental Concepts
Introduction to stresses:
Review of fundamentals: forces and their distributions on a body;
Static analysis: Internal Moment Equations via Free-body diagrams (Review);
Definition of Stress
Stress Components at a Point
Stress
Lecture 6
Two Dimensional Problems in Elasticity
In this lecture, the following topics will be discussed:
Elasticity Problems: What are the unknowns and what
are the governing equations
Boundary Conditions
Plane Problems: Plane Stress and Plane Strain
Air
Lecture 2
Mohrs Circle
In this lecture, the following topics will be discussed:
Mohrs Circle
Transformation of 3-D Stress
Simplification of 3-D Stress Transformations
Principal Stresses (Eigenvalue Problem) (3-D stress)
1
MOHRS CIRCLE FOR 2-D STRESSES
A t
Lecture 3
Stress, strain, displacement
Outline of Lectures
This lecture introduces the idea of a displacement field in a deformed body,
followed by a discussion of normal and shearing strain, and strain tensor.
Next, we derive the Compatibility Equations
Lecture 4
Engineering Materials, Hookes Law
Outline of Lectures
In this lecture, the following topics will be discussed:
Ductile and Brittle behavior
Typical stress-strain behavior of ductile materials
The idea of a constitutive relation is introduced, w
Lecture 5
Strain Energy
To Outline of Lectures
In this lecture, the following topics will be discussed:
Strain Energy
Components of the Strain Energy
Saint-Venants Principle
1
Strain Energy
Work done by external forces is stored in the body as strain en