Stress Transformation
Civ E 270
Khattak, N
3 Dimensional Stress State
y
In a Cartesian coordinate system, a total of nine
stress components are required to completely
describe the state of stress on a cubic element.
yz
yx
y
xy
zy
However, when looking at
Beam Deflections
Civ E 270
Khattak, N
Deflection of Beams by Moment-Area Method
The moment area method provides a graphical technique for evaluating deflection on a beam due
to bending. The application of this method requires calculating the areas associa
3| University of All] H'ta
Department of Civil and Environmental Engineering
Cir E HI]
Laboratory ll]
. ’ame.‘ 121).:
Date: iﬂark:
L of:- Section:
BEAM DEFLIEIC' TIDNS
113.1 OBJECTIVES
c To measure the deﬂections of a member due to bending.
a To review t
Torsion
Civ E 270
Khattak, N
Torque
A moment that tends to twist a member about its longitudinal axis is called a torque.
T
T
Sign Convention
The torque can be shown with a rotating arrow OR a straight double arrow. Using the right hand
rule, if you curl
Bending
Civ E 270
Khattak, N
Bending Deformations
Axial Loads
Axial Stresses
Torsional Loads (Torques)
Torsional or Shear Stresses
Bending Loads
Bending Stresses
Bending results from equal and opposite couples acting in the same longitudinal plane.
M
M
Co
Pressure Vessels
Civ E 270
Khattak, N
Thin Walled Pressure Vessels
Cylindrical and spherical vessels are used in the industry as coolers, boilers and tanks. Thin
wall refers to a vessel having an inner radius to wall thickness ratio of 10 or more, i.e. r/
Combined Loadings
Civ E 270
Khattak, N
Stresses Under Combined Loadings
Loadings
Stresses caused by loads
Axial Load, P
p =
P
A
Bending Moment, M
b =
My
I
Torque, T
T =
T
J
Shear Force, V
v =
VQ
It
Assuming small deformations and elastic material, the li
Assignment 4
CIV E 270
1
Assignment 4
CIV E 270
2
Assignment 4
CIV E 270
Note: Option to solve either 4-43 OR 4-44
3
Assignment 4
CIV E 270
Note: Option to solve either 4-43 OR 4-44
4
Assignment 4
CIV E 270
5
Assignment 4
CIV E 270
5
Shear
Civ E 270
Khattak, N
Shear Stress in Beams
Beams support both moment and shear loading
Bending Moment
(Loads cause moment which
cause bending)
Transverse Shear
(Transverse loads cause
transverse shear)
Longitudinal Shear
Transverse Shear
Transverse
Axial Loads
Civ E 270
Khattak, N
Elastic Deformation of an axially loaded member
For the case of a constant load, cross sectional area and homogeneous material (E is constant)
=
Stress
Strain =
P
A
P
P
L
L
In the elastic region;
= E
P
= E
A
L
=
PL
AE
I
Assignment 1
1
CIV E 270
Find support reactions from
equilibrium equations
By=6.67 kN
Ay=9.33 kN
(6000)(2) N
1m
4000 N
1m
1m
V(kN)
9.33 kN
1.55 m
m
9.33-(6)(2)=-2.67
-2.67-4 = -6.67
M(kN.m)
(9.33)(1.55)/2=7.23
7.23-(2.67)(2-1.55)/2=6.67
6.67-(6.67)(1)=0
A
*8—20. Determine the maximum and minimum normal 100 kN
stress in the bracket at section (1—5: when the load is applied 15 mm
“x : 300 mm, 7 ‘ ‘ ‘1‘ (Z -
( '15mm’“>:_ \, , /
(K
200 mm "3
lSO mm
Consider the equilibrium of the FBD of the top cut s
University of Alberta
Department of Civil and Environmental Engineering
Civ E 270
Laboratory 3
Name:
I.D.:
Date:
Mark:
Lab Section:
COMPRESSION TEST
3.0
3.1
3.2
OBJECTIVES
To obtain stress vs. strain diagrams for concrete and wood.
To plot a stress vs. st
University of Alberta
Department of Civil and Environmental Engineering
Civ E 270
Laboratory 2
Name:
I.D.:
Date:
Mark:
Lab Section:
TENSION TEST
2.0 OBJECTIVES
To illustrate different types of tensile behaviour by performing tension tests on aluminum
and