MANUKAU INSTITUTE OF TECHNOLOGY
School of Mechanical Engineering & Trades
DIPLOMA IN MECHANICAL ENGINEERING

Beam Reactions

OBJECT

1.To determine both the theoretical and actual support reactions of a simple vertically loaded beam, showing that the loadings on the supports are directly proportional to the distances of the loads from the supports; thus illustrating the principle of the moments of forces. 2.To determine the beam support reactions for a horizontal beam carrying vertical loads at positions across the span.

APPARATUS

Two support stands, beam of uniform round bar, load hangers, known loads, two spring balances with suitable supports for beam.

1.PROCEDURE

•Assemble the apparatus as a simply supported beam with a span of 900mm. Adjust the equipment so that the beam is horizontal, the spring balances, and beam supports are vertical. Note the spring balance readings for each support with just the bar in place. •Place a 10N load onto the load hanger and suspend it directly beneath one of the spring balances. Note both spring balance readings. •Next move the mass hanger 100mm along bar and note both spring balance readings. Repeat this procedure of incremental movement and readings until mass hanger is suspended directly under the spring balance at the opposite end of beam to the initial step. •Calculate the theoretical beam reactions and use a graph to show the comparison of the two sets of data.

2.PROCEEDURE

•Suspend the beam to give a span of 900mm.
•Place loads as shown in the diagrams below and record the measured beam reactions. •Calculate the theoretical beam reactions and use a graph to show the comparison of the two sets of data. BEAM LOADING PATTERNS

a)

10N20N
250mm
750mm

b)

20N 20N
500mm
750mm

c)

10N 15N10N
150mm

400mm

800mm

RESULTS

Record the results for each part of the lab work into separate tables.

...Introduction
A bendingmoment is simply defined as “the algebraic sum of the moments of all the forces which induces bending of an element” (1). The aim of this assignment is to work out the bendingmoment in a simply supported beam when different concentrated loads are applied to it. A simply supported beam is a structure, usually with a straight profile supported at the ends, often pinned on one side and simply supported or on a roller on the other. There will be three series of loads applied to this beam & the findings will be recorded. The results will then be compared with the theoretical bendingmoment & the reasons for any variation explained.
The main reason for the experiment to be conducted is to examine, not only the accuracy of the testing equipment, but also the accuracy of bendingmoment calculations and diagrams compared to a real-world assessment. It will hopefully prove that “the bendingmoment at a cut section is equal to the algebraic sum of the moments acting to the left or right of the section”. (2)
After this introduction, there will be a little background information about this experiment and its apparatus, followed by a breakdown of the experimental procedure. Then, there will be the displayed results before a comparison with the theoretical results that have been...

...1.0 OBJECTIVE
1.1 To examine how bendingmoment varies with an increasing point load.
1.2 To examine how bendingmoment varies at the cut position of the beam for various loading condition.
2.0 LEARNING OUTCOMES
2.1 To application the engineering knowledge in practical application
2.2 To enhance technical competency in structural engineering through laboratory application.
2.3 To communicate effectively in group.
2.4 To identify problem, solving and finding out appropriate solution through laboratory application.
3.0 THEORY
3.1 There are a number of assumptions that were made in order to develop the Elastic Theory of Bending. These are:
* The beam has a constant, prismatic cross-section and is constructed of a flexible, homogenous material that has the same Modulus of Elasticity in both tension and compression (shortens or elongates equally for same stress).
* The material is linearly elastic; the relationship between the stress and strain is directly proportional.
* The beam material is not stressed past its proportional limit.
* A plane section within the beam before bending remains a plane after bending (see AB & CD in the image below).
* The neutral plane of a beam is a plane whose length is unchanged by the beam's deformation. This plane passes through the centroid of the cross-section.
3.2 In...

...Objective
The objective of this experiment is to compare the theoretical internal moment with the measured bendingmoment for a beam under various loads.
Introduction and Background
Theory
Definition of a Beam
Members that are slender and support loadings that are applied perpendicular to their longitudinal axis are called beams. Beams are important structural and mechanical elements in engineering. Beams are in general, long straight bars having a constant cross-sectional area, often classified as to how they are supported. For example, a simply supported beam is pinned at one end and roller-supported at the other, a cantilevered beam is fixed at one end and free at the other, and an overhanging beam has one or both of its ends freely extended over the supports.
Figure 1: Types of beams
Types of Internal Loading
The design of a structural member, such as a beam, requires an investigation of the forces acting within the member which is necessary to balance the force acting externally on it. There are generally four types of internal loading that can be resisted by a structural member:
Figure 2: Types of Loadings
A. Normal Force, N
This force acts along the member’s longitudinal axis and passes through the centroid or geometric centre of the cross-sectional area. It acts perpendicular to the area and is developed whenever the external loads...

...
Lab report
SHEAR FORCE & BENDINGMOMENT
Bachelor (Hons) of Civil Engineering
Course: Structures l (ECS3213)
Lecturer: Ir Pan
Submission date: 07-11-2013
Group 8: Members
No.
Name
Student ID
1
Diallo Mamadou Aliou
SCM-014804
2
Balmeiiz Abilkhaiyrova
SCM-014742
3
Elmogdad Merghani Mohamed Elhag
SCM-017223
4
Omar Mohamed Abdelgawwad
SCM- 018031
5
Salah Mohammed Alesaei
SCM-015473
6
Ali Abdulrahman Mohammed
SCM-008879
7
Kasem Heiazi
SCM-017913
Contents
A. Introduction: 3
B. Objectives: 4
C. Theory: 4
D. Apparatus: 6
E. Procedures: 7
F. Results: 9
G. Calculations: 9
H. Shear Force Experiment Discussion: 14
I. BendingMoment Discussion: 15
J. Conclusion: 15
K. References 16
A. Introduction:
It is important to know how the shear forces and bendingmoments vary along the length of a beam that is being designed. Graphs are used to describe the change of shear forces and moments. These graphs are called shear and moment diagrams. Employing these diagrams, the maximum and minimum shear and moment are easily identified and located.
Constructing shear and moment diagrams is similar to finding the shear and moment at a particular point on a beam structure. However, instead of using an exact location, the location is a variable distance 'x'. This allows the shear and...

...BEAM DESIGN FORMULAS
WITH SHEAR AND MOMENT
DIAGRAMS
2005 EDITION
ANSI/AF&PA NDS-2005
Approval Date: JANUARY 6, 2005
ASD/LRFD
N DS
®
NATIONAL DESIGN SPECIFICATION®
FOR WOOD CONSTRUCTION
WITH COMMENTARY AND
SUPPLEMENT: DESIGN VALUES FOR WOOD CONSTRUCTION
American
Forest &
Paper
Association
x
w
Wood
American Wood Council
American Wood Council
R
R
2
2
V
Shear
V
Mmax
Moment
American
Forest &
DESIGN AID No. 6
DESIGN
Paper
Association
BEAM FORMULAS WITH
SHEAR AND MOMENT
DIAGRAMS
The American Wood Council (AWC) is part of the wood products group of the
American Forest & Paper Association (AF&PA). AF&PA is the national trade
association of the forest, paper, and wood products industry, representing member
companies engaged in growing, harvesting, and processing wood and wood fiber,
manufacturing pulp, paper, and paperboard products from both virgin and recycled
fiber, and producing engineered and traditional wood products. For more information
see www.afandpa.org.
While every effort has been made to insure the accuracy
of the information presented, and special effort has been
made to assure that the information reflects the state-ofthe-art, neither the American Forest & Paper Association
nor its members assume any responsibility for any
particular design prepared from this publication. Those
using this document assume all liability from its use....

... Bending of a Channel Section
Experiment Two: Stiffness Report from laboratory work performed on 12 May 2011 as a part of the unit of study CIVL2201 Structural Mechanics
Abstract
This report has been written to describe an experiment performed on a channel section examining the stiffness of the beam through two differing types of deformation – curvature and deflection. The aim of the experiment was to determine the value of the flexural rigidity (EI) in two different ways; using the curvature, k, and the mid-span deflection. The testing method used for the experiment is described. The experiment found that the EI values calculated were as follows: - EIcurv = 1.76E+10 Mpa.mm4 when calculated using the curvature, k. - EIdefl = 1.77E+10 Mpa.mm4 when calculated using the mid-span deflection.
Bending of a Channel Section
Table of Contents
Abstract ................................................................................................................................. 1 Introduction ........................................................................................................................ 3 Test Method ......................................................................................................................... 3 Diagram of the test setup ........................................................................................................ 3 ....

...and moment for:
a. Simply supported beam
b. Simply supported beam with one end overhanging
c. Simply supported beam with both ends overhanging.
2. To calculate shear force and moment using influence line
3. To determine maximum shear force and moment
4. Calculate Absolute Maximum Moment (MMM)
4.1 INTRODUCTIONS:
Influence line is to:
Analysis a structure due to moving load along the beam.
Show the changes in reaction, shear stress,moment and displacement in certain point in structure when applied a unit load.
Determine the greatest position the greatest value of live load in beam.
4.2 DIFFERENCES BETWEEN INFLUENCE LINE DIAGRAM (ILD) AND BMD (BENDINGMOMENT DIAGRAM)
INFLUENCE LINE DIAGRAM
(ILD)
BENDINGMOMENT DIAGRAM (BMD)
a) Static and Moving Load
b) Diagrams show only one point on the beam.
c) Calculations based on the virtual load.
d) Straight line only
e) Calculations do not refer to reactions of beam.
f) Unit: m
a) Static load only.
b) Diagram shows the moment at all points on the beam.
c) Calculations based on real loads.
d) Straight lines and curves.
e) Calculations based on the SFD.
f) Unit : kNm
4.3 BASIC CONCEPT TO DRAW INFLUENCE LINE DIAGRAM (ILD)
1 unit
x
A B C
a b
RAY = [L-x]/L 1-x/L RCY=x/L
4.3.1 REACTION
ILD RAY L/L
b/L
[+]...

...EXPERIMENT : CONTINUOUS BEAM
1.0 Learning outcome:
1.1 Determine the magnitude of the fixing moment in a continuous beam by experiment and
to compare this with the value predicted by theory.
2.0 Apparatus/Equipment:
2.1 Aluminium
2.2 Brounze
2.3 Weight
2.4 Dial gauge
Weight Dial gauge Aluminium Brounze
3.0 Safety and health:
3.1 Make sure the student follow the laboratory or workshop safety regulator.
3.2 Experiment must be conduct by lecturers or experience lab assistance.
3.3 Always wear appropriate protective clothing.
3.4 Be familiar with the location of emergency equipment-fire alam ,fire
extinguisher,emergency eye wash and safety shower.
3.5 Always wash hand and arms wit soap and water before leaving the work area.
3.6 Never perform unauthorized work,preparation or experiments.
4.0 Theory:
1.Horizontal structural member used to support horizontal loads such as floors, roofs, and decks.
2. Consider a simply supported beam of length, L.
3. The The cross section is rectangular with width b and height h cross section is rectangular, with width, b, and height, h.
4. Beams have been used since dim antiquity to support loads over empty space, as roof beams supported by thick columns, or er of the approximate methods...