CE2033 (5 ch) Structural Analysis
Determine the horizontal deflection of joint C in the
pin-jointed Truss shown. Use the method of real
work. All members have the same cross sectional
area and are mad
CE2033 (5 ch) Structural Analysis
Determine the deflection of the hinge
at C and the joint rotation at B for the
braced frame. EI is constant in all
members.
NOTE:
Since member BCD contains a hinge
it
CE2033 (5 ch) Structural Analysis
Determine the displacement
at C and the slope at B. EI
is constant. Use the conjugate beam method.
Develop M(x) using normal
shear and bending moment
calculations.
Fo
CE2033 (5 ch) Structural Analysis
In both examples above, a unit rotation is applied at the point where we want our maximum bending moment and then sketch out how all the beams and columns would defle
CE2033 (5 ch) Structural Analysis
Determine the vertical deflection under the
load P. The load is applied gradually from zero
to a value of P. Use the method of real work.
V(x)! = -P
M(x)! = -Px
We!=
CE2033 (5 ch) Structural Analysis
Determine the member end moments for the
beam and loading indicated using moment distribution.
Prodecure
1. Evaluate stiffnesses, distribution factors,
carry over fac
CE2033 (5 ch) Structural Analysis
Reaction @ A
Reaction @ B
BMD @ B
BMD @ centreline
Shear @ C
Shear @ centreline
for the beam shown.
Also determine each
maximum value.
-RAmax! = 20(-1/3) + 20(-
CE2033 (5 ch) Structural Analysis
Virtual Work
From basic physics we know that the work done done by a force or moment is
equal to that force or moment multiplied by the distance (for forces) or rotat
CE2033 (5 ch) Structural Analysis
Determine expressions for shear force and bending moment across the footing.
It can be seen that there is on discontinuity in loading when moving from the left hand
e
CE2033 (5 ch) Structural Analysis
Conjugate (analogous) Beam
Introduction
method was developed and presented in a paper in 1868 by Otto Mohr
Description
If a conjugate (analogous) beam is loaded with
CE2033 (5 ch) Structural Analysis
The Structural Design Process
1. Arrange the general layout of the structure to satisfy the owner's requirements
2. Carry out preliminary cost studies of alternative
CE2033 (5 ch) Structural Analysis
Question
Determine the reactions for the
structure shown. Also determine the axial force, shear &
moment at each end of the
members
Solution
If we consider the overal
CE2033 (5 ch) Structural Analysis
Absolute Maximum Shear & Bending Moment
will only consider simply supported beams subjected to moving wheel loads.
Shear
Maximum is at a point next to one of the rea
CE2033 (5 ch) Structural Analysis
Positive Moments
imply point lies below tangent line
Examples
Determine the beam rotation at
A and the deflections at F and C.
Since the problem is symmetric the rota
CE2033 (5 ch) Structural Analysis
Influence Coecients
help to explain the relationship between member displacements and member forces
influence coefficients could be described as the response at one
CE2033 (5 ch) Structural Analysis
The virtual moment curve is always either a straight line or a series of straight lines. As
a result any line segment for the m diagram from point j to k can be repre
CE2033 (5 ch) Structural Analysis
Deflections
"It is probably obvious by this time that these deflections, be they large or small, generate the forces of resistance which make a solid hard and stiff a
CE2033 (5 ch) Structural Analysis
In addition, free body diagrams can be drawn for
each of the individual pieces that make up the frame.
If you consider just the free bodies from the individual
pieces
CE2033 (5 ch) Structural Analysis
4. Force frame to sway.
Consider the case where the problem frame is given a
lateral deflection or sway. In this case the fixed end moments that are set up in AB and
CE2033 (5 ch) Structural Analysis
Shear & Bending Moment Diagrams
In general, an engineer would like to know the variation in shear and bending moment
over the length of a beam. This information would
CE2033 (5 ch) Structural Analysis
Member BC is a high strength, strand
wire, steel cable for which EA = 7337 K
and the maximum recommended design
load is 39 K; member AB is a steel
beam for which EI =
CE2033 (5 ch) Structural Analysis
Using virtual work to calculate the end rotations due the real loading on the statically determinate base structure.
A! = (1/EI)[L(0.281wL)() + (L)(-0.281wL)(0.8125)]
CE2033 (5 ch) Structural Analysis
Consider the following:
External work by applying P: ! ! ! ! ! ! ! We = P11
External work, P kept on beam, by applying M:! ! We = P12 + M22
Total external work done i
CE2033 (5 ch) Structural Analysis
Procedure
2. Carry out actual moment distribution and plot results.
AB
BA
BC
CB
CD
DC
Carry over factor
0.5
<=0.0 0.5=> <=0.5 0.5=> <=0.0
=>
Distribution factor
1.000
CE2033 (5 ch) Structural Analysis
Elastic Strain Energy (internal work) - Bending Moment
From Strength of Materials
d/dx = M/EI
d = (M/EI)dx
The internal work associated with dx is
dWi = Md
dWi = M[(M
CIVL 3705
Mechanics of Structural Materials and Components
Department of Civil and Resource Engineering, Dalhousie University
Assignment 2
Due: Oct. 5 by 5 pm in the assignment box
1. The two member f
CIVL 3705
Mechanics of Structural Materials and Components
Department of Civil and Resource Engineering, Dalhousie University
Assignment 3
Due: Oct. 19, 5 pm in the assignment box
1. Draw the moment d
CIVL 3705
Mechanics of Structural Materials and Components
Department of Civil and Resource Engineering, Dalhousie University
Assignment 1
Due: Sep. 21 by 5 pm in the CIVL 3705 assignment box next to