CE2033 (5 ch) Structural Analysis
Selecting Section to Calculate Force
in "cg"
The figure illustrates three different
sections that could be used to separate the truss into two independent
pieces and, at the same time, cut
the element for which the intern
CE2033 (5 ch) Structural Analysis
It is only when the truss is taken apart and equilibrium of one of its parts is considered
that internal forces show up. The diagram shows free body diagrams for two of the truss
elements. When they are isolated from the
CE2033 (5 ch) Structural Analysis
Newmark's Method
Introduction
method was developed and presented in a paper in 1943 by N.M. Newmark
Description
Carry out a conjugate beam analysis but replace the M/EI curve on the conjugate beam
with a set of equivalen
CE2033 (5 ch) Structural Analysis
Relationships between Loading Shear & Bending Moment
There are explicit relationships between
the loading, shear and bending moment.
1. Consider a beam carrying a general
type of distributed loading.
2. Remove a small por
CE2033 (5 ch) Structural Analysis
Extra Examples
Draw the influence line for the bending
moment at point "c". Based on your influence line, determine the maximum bending
moment that can be generated at "c" by the
wheel loads specified. Do not bother to
ch
CE2033 (5 ch) Structural Analysis
As we we continue to move the loads across the beam, stopping each time one of
the loads changes from one slope to the next. Each time this happens we recalculate V and recalculate the actual V only where the sign of V ch
CE2033 (5 ch) Structural Analysis
Moment Area
Introduction
method presented in 1873 by Charles E. Greene
useful in problems where the bending moment relation is discontinuous
From "Strength of Materials"
dy/dx = M/EI
dy/dx = = A B(M/EI)dx + C
equals the
CE2033 (5 ch) Structural Analysis
Method of joints
based on particle equilibrium
Fx = 0
Fy = 0
good if want to determine "all" members forces for a truss
Procedure
Determine truss reactions (if required)
Draw free body diagram of joint to be considere
CE2033 (5 ch) Structural Analysis
General Regulation on Conduct
Part of the UNB's Mission is to provide an environment conducive to the development of the whole person. All members of the University community - staff, faculty,
students and administrators
CE2033 (5 ch) Structural Analysis
Determine the
maximum shear at
the section shown
(7.5 m from A) for
the wheel loads
shown.
Rather than use
the procedure
used in the previous calculations for
this example, we
use a slightly different approach.
What are t
CE2033 (5 ch) Structural Analysis
a)
If the two forces are parallel,
then sum forces perpendicular to
them. This will eliminate both
and allow you to solve for the
other unknown which is what
you were looking for.
b)
If the two forces are not parallel,
th
CE2033 (5 ch) Structural Analysis
!
Smith, J.C., Structural Analysis, Harper and Row, 1988, page 1.
Load Combinations
buildings and their structural components shall be designed to have sufficient
strength and stability so that the factored resistance is
CE2033 (5 ch) Structural Analysis
!
!
!
R D + VC = 0
VC = -RD
! = -x/4
From previous slide, when load moves onto DB there no now forces acting on AD.
VC = 0; MC = 0
Mller-Breslau Principle
"The influence line for any force quantity in a structure is repr
CE2033 (5 ch) Structural Analysis
Introduction to Frames Analysis
Frames are systems built up from a number of rigid elements, one of which has to be a
three or more force element. If all the elements are two force elements then we are
back to a basic tru
CE2033 (5 ch) Structural Analysis
Energy Methods
Real Work
Definitions
Work!
!
the product of force and distance when the force acts on a body
and moves its point of application by that distance (ie. We = P)
Energy! ! ! the capacity to do work (ie. KE =
CE2033 (5 ch) Structural Analysis
Selecting Section to Calculate Force in "be"
This figure illustrates two possible sections
that will separate the truss into two independent pieces and, at the same time, cut
"be". Unfortunately, it can also be seen that
CE2033 (5 ch) Structural Analysis
Determine the influence lines
for the shear and bending
moment at n-n.
Use Mller-Breslau to determine the influence line for the
reaction at A.
Fy! = 0 [+]! !
!
The accompanying free body diagram
RA - 1 + Vn = 0!
Vn! = 1
CE2033 (5 ch) Structural Analysis
"Structural analysis is the determination of the reactions, member forces and deformations of a structure due to applied loads and environmental effects.
Structural Design involves
(1) arranging the general layout of the
CE2033 (5 ch) Structural Analysis
A home owner has decided to build a
bridge across a brook on the back 40
and needs to know what shear force and
bending moment to design it to.
His pick up is designed to carry 11.1 kN
on the front tires and 12.9 kN on th
CE2033 (5 ch) Structural Analysis
Again, where should we position the
loads to maximize the bending moment. Hopefully, it is obvious that
one of the two loads should be positioned whee the influence line is
maximum. These two options are
shown below.
MC!
CE2033 (5 ch) Structural Analysis
Determine the maximum load "P" that can be applied to
the boom trailer if the maximum force that the piston
can exert is 20,000 N and the weight of the trailer plus
boom is 6,000 N centred at c.g.
Point A may be considere
CE2033 (5 ch) Structural Analysis
Now consider a beam that is subjected to a
unit load located at an arbitrary point along
the length and provide an arbitrary displacement at the location of the force for
which we want to determine the influence
line.
RbB
CE2033 (5 ch) Structural Analysis
Stiffness Influence Coefficients
"A stiffness influence coefficient for a
structure, kij, is defined as the force
at point I resulting from a unit displacement imposed at joint j."
Implicit in this definition is that all
CE2033 (5 ch) Structural Analysis
Consider this very simple example of applying MllerBreslau to determine the influence lines for shear and
bending moment at the quarter point of this simply
supported beam.
For the shear diagram we impose a vertical disco