Change in slope and tangential deviation between points A and B

Moment-Area Method

Beam and moment curve

M/EI curve between points A and B

Moment Area Theorems
•The change in slope between any two points on a smooth continuous elastic curve is equal to the area under the M/EI curve between these points •The tangential deviation at a point B on a smooth continuous elastic curve from the tangent line drawn to the elastic curve at the second point A is equal to the moment about B of the area under the M/EI curve between these two points.

Moment-Area Method

Horizontal, therefore the vertical distance between tangent line and elastic curve are displacements

Cantilever, point of tangency at fixed support

Moment-Area Method

Symmetric members with symmetric loading, point of tangency at intersection of axis of symmetry and elastic curve

Moment-Area Method

Point of tangency at left end of member AB
t BA L tan θ A = θ A in radians tan θ A =

θA=

t BA L

Caution 2.The theorem is applicable for continuous elastic curve 3.Presence of hinge breaks continuity of elastic curve 4.If hinge is present on beam or a frame – then work on either side of hinge (left or right side)

P 9.6 (3rd Edition)

Derive the equations for slope and deflection for the beam shown. Determine the slope at each support and value of deflection at mid span. Hint: Take advantage of symmetry; slope is zero at midspan.

P 9.13

Compute the slope at support A and the deflection at point B. Treat the rocker at D as a roller. Express the answers in terms of EI.

P 9.15 Determine the slop and deflection of point C...

...
FACULTY OF ENGINBERING AND BUILT ENVIRONMENT
BEng (Hons) Civil Engineering
Structure I
Deflection
Contents:
Introduction 3
Objectives 3
Apparatus 4
Procedure 4
Results 4
Discussion 7
Conclusion 7
References 8
Introduction:
The deflections of a beam are an engineering concern as they can create
an unstable structure if they are large. People don’t want to work in a
building in...

...The Report of Deflections of Beams and Cantilevers
Summary:
There are four parts in this big experiment, including deflection of a cantilever, deflection of a simply supported beam, the shape of a deflected beam, and circular bending. In these four parts, a same set of laboratory instrument and apparatus is used, concluding a bracket, a moveable digital dial test indicator, U-section channel, moveable knife-edge, and three material beams: brass,...

...Experiment 7: Deflection of beams (Effect of beam length and width)
1. OBJECTIVE
The objective of this laboratory experiment is to find the relationship between the deflection (y) at the centre of a simply supported beam and the span, width.
2. MATERIALS - APPARATUS
Steel Beams, Deflection measuring device, 500g weight
3. INTRODUCTORY INFORMATION
The deflection of a beam, y, will depend on many factors such as: -
The...

...1.0 BACKGROUND OF STUDY
The deflections of a beam are an engineering concern as they can create an unstable structure if they are large. People don’t want to work in a building in which the floor beams deflect an excessive amount, even though it may be in no danger of failing. Consequently, limits are often placed upon the allowable deflections of a beam, as well as upon the stresses.
When loads are applied to a beam their originally straight axes become curved....

...Intro: This assignment consists of predictions to theories on measuring and comparing results on deflection on a beam.
Intro: This assignment consists of predictions to theories on measuring and comparing results on deflection on a beam.
Beam Defection Experiment
1) This graph and its table below showed the resultant forces which were achieved when the test on the relationship between deflection (Y) and the spacing achieved (L3) using a...

...Slope deflection method
From Wikipedia, the free encyclopedia
The slope deflection method is a structural analysis method for beams and frames introduced in 1914 by George A. Maney.[1] The slope deflection method was widely used for more than a decade until the moment distribution method was developed.
Contents
[hide]
1 Introduction
2 Slope deflection equations
2.1 Derivation of slope deflection equations
3 Equilibrium...

...at a specified length across the beam and then measuring deflection. The measuring device was set a specified distance from the clamped end. The following procedure was employed for both the steel and aluminum beam. The second part of the experiment required placing a single known mass at various lengths across the supported beam and then measuring the resulting deflection. This method was only completed for the steel beam. The deflections from both...

...Laboratory Three: Parallam Beam Deflection
Lab Group - 1st Mondays, Late: Jesse Bertrand, Ryan Carmichael, Anne Krikorian, Noah Marks, Ann Murray Report by Ryan Carmichael and Anne Krikorian
E6 Laboratory Report – Submitted 12 May 2008 Department of Engineering, Swarthmore College
Abstract:
In this laboratory, we determined six different values for the Elastic Flexural Modulus of a 4-by10 (100” x 3.50” x 9.46”) Parallam wood-composite test beam. To accomplish this, we...