HomeworkT
The stress distribution in a thin wide steel plate [E = 200 GPa and v = 0.30J with a central circular
hole is given by Eqs. (3.42) when the plate is subjected a uniaxial tensile or compressive load'
Determine the error made in the determination
Homework 10
A Helium-Neon laser produces light of wavelength = 632.8 nm. Determine:
1. The frequency of this light
2. The wavelength of this light when it propagates through a glass plate of index of
refraction n=1.522
3. The velocity of propagation in th
2.2
Given the disPlacement field:
u = [x 2 + Y+ + bYzz+ YzJ[1O-:i
v= ()ry + xz + 3xzz)[10-J
+
w = [y4 +4Y3 2zz)(lo-3)
2.3
(2'2J
Compute the associated strains at point (1,2,3). Compare the results obtained by:using Eqs,
and [2,3) with those obtained by us
Homework 9
An aluminum panel (E = 70 GPa, = 0.33 ) under a uniaxial residual stress o in the ydirection is investigated by the hole drilling technique. A strain gage is placed along the x-axis
and subsequently an 8 mm diameter hole is drilled with its cen
Homework 4
A cylindrical pressure vessel of inner and outer radii a and b is subjected to internal pressure p
and the displacements ua and ub on the inside and outside surfaces are measured. Determine the
Youngs modulus and Poissons ratio of the material
Homework Assignment No.
cfw_
.
At a point in a stressed body, the Cartesian components of stress are oxx : oyy : 75 MPa , 6rz=
- 30 MPa, r*y : 0, r*= 45 MPa and rr*- 75 MPa. Determine the normal and shear stress on
a plane whose outer
cos (n,
2,
1
normal
THEORY OF ELASTICITY
HOMEWORK ASSIGNMENT #4
Instructor: Prof. Gianluca Cusatis
DUE THURSDAY MARCH 12, 2015
1. The thin-walled cross-section shown below represents a highly idealized
airfoil structure:
Homework 6
CivEnv 495
Due Thursday, November 12
1.
The floor loading in a steel building has a superimposed live load of 270 psf (always assume
load is unfactored unless noted otherwise). For a deck span of 96 with normal weight
concrete and studs spaced
CHAPTER
BASIC EQUATIONS
3.
1
3
. PLANE ELASTICITY
Formulation of problem
In the general 3-D problem there are 15 unknowns to be determined
at
a point:
6 stress
components:
o1, oy,
6 strain
components:
t1, ty,
3 displacement
C,2, xxy,
xyz, xzx
t-z, Txy, Ty
9/30/2014
Lecture 2
Review
1
9/30/2014
State of Stress at a Point
Stress Components along Coordinate Directions
z
z
x
y
2
9/30/2014
Equations of Equilibrium
Transformation of Stress Tensor
3
9/30/2014
Two-Dimensional State of Stress
Stress Transformation
Stress-Strain Relations
Assumptions: Continuousmedium
Linearity of stress vs. strain
General linear stress-strain relation
6ij - Ci;u sg
or, in contracted notation and in matrix form
6oy
oz
xy,
xr*
\xY
Er
C* C* Cro C,
c, c* cro c^
C, C* C.o C ,
I !; Co, C
Determination of Sphere Radius by Shadow Moir Imaging
November 11, 2014
Objective:
The objective of this lab is to demonstrate optical methods of displacement and contour
measurement, specifically a form of geometric Moir for measuring the out-of-plane
co
Determination of Material Fringe Value
An epoxy disk, 3 in. in diameter and 0.+0 in. thick, was loaded under diametral
compression of P = 500 lb and the fringe patterns below were obtained
photographically. Determine the maximum fringe order at the center
Homework 13 (2014)
A urethane rubber disk 100 mm in diam. and 10 mm thick is loaded under diametral compression
with a load P = 275 N. The disk is coated with an array of 10 horizontal lines/mm and using a
similar master array the following moir fringe pa
Troblolrr Fflr
The following data were obtained from a series of tests conducted on precracked
specimens of thickness
I
mm.
':,
't1
,.
length
Critical load
Critical displacement
P(td.cfw_)
u(mm)
30.0
4.00
0.40
40.0
3.50
0.50
50.5
3.r2
0.63
Crack
a(mm)
6t.
Northwestern University
Department of Civil & Environmental Engineering
Civ_Env 319 Theory of Structures II
Experiment 1 Experimental Stress Analysis Thin-Walled Pressured Vessel
Objectives:
1. To familiarize the students with experimental stress analysis
Northwestern University
Department of Civil & Environmental Engineering
CivEnv 319 Theory of Structures II
Problem Set 6 Influence Lines
6.1. Refer to Figure 6.1, construct the influence lines for reactions at A and B, shear at C, moment at C, shear at D,
Northwestern University
Department of Civil & Environmental Engineering
CivEnv 319 Theory of Structures II
Problem Set 5 Moment Distribution Method
Use moment distribution method and Excel unless otherwise stated to analyze all the problems in this proble
Northwestern University
Department of Civil & Environmental Engineering
CivEnv 319 Theory of Structures II
Problem Set 4 Slope Deflection Method
Use slope deflection method to analyze all the problems in this problem set.
4.1.
4.2.
4.3.
4.4.
4.5.
Construc
Northwestern University
Department of Civil & Environmental Engineering
CivEnv 319 Theory of Structures II
Problem Set 3 Indeterminate Analysis Plane Frames
3.1. Construct the final bending moment diagram for the structures shown in Figure 2.1 for the fol
Northwestern University
Department of Civil & Environmental Engineering
CivEnv 319 Theory of Structures II
Problem Set 2 Indeterminate Analysis Plane Trusses
1.1. For the truss shown in Figure 1.1, compute the reactions and final member forces for each of
Northwestern University
Department of Civil & Environmental Engineering
CivEnv 319 Theory of Structures II
Problem Set 1 Approximate Analysis
1.1. Approximate the analysis for the frame shown in Figure 1.1 due to gravity loads only. Draw the final bending
CIV_ENV 495-0-26 Homework 5
Solve the hypar problem below using the force density method. Report the
coordinates at each node and the forces in each member for the following
cases:
1)
2)
3)
Uniform densities q=10
Uniform densities q=20
Edge cables densiti
CE 495: Graphics Statics Homework
Due: May 14, 2013
Q1. For the given optimal (minimal volume) structure, using graphic statics, draw and clearly label
the reciprocal form and force diagrams. Then, graphically determine the force in each member and
indica
CIV_ENV 495-0-26 Homework 3
Download the 99 line Matlab code at:
http:/www.topopt.dtu.dk/
a. Tab Applet and Software and MATLAB program
b. Download the matlab code top.m
c. Run the default MBB-example problem typing
top(60,20,0.5,3.0,1.1) in the Matlab c
CIV_ENV 495-0-26 Homework 2
For the frame below calculate the areas of the steel members
required to achieve a deflection at the top of the building of 1.2 ft
(H/1000).
The total building height is 1200ft, the wind loads are in kips and
lengths are in ft
CIV_ENV 495-0-26 Homework 1
1. For the frame below calculate the minimum volume of steel required
in the design using Maxwells theorem and the deflection of the truss
in the middle using the principle of virtual work:
?
2. For the three trusses a), b), c)
09’ O) The thin walled cross section depicted in the ﬁgure below is subjected to a 1 kNm
torque; ﬁnd the shear stress and the angle of twist per unit length. Also compute and
plot the warping function.
a=150mm
r=75mm
t=6mm
6:80 GPa
Area of midsurface: