MEM23061A Test Mechanical Engineering Materials
Lab. BEAM BENDING
The bending of beams is one of the most important types of stress in engineering. Bending is more likely to be a critical stress than other types of stress - like tension, compression etc. In this laboratory, we will be determining the Modulus of Elasticity E (also called Young's Modulus) of the various materials and using Solid Edge to determine the Second Moment of Area for the different cross-sections.

[pic]

Equations
Use units: Force (N), Length (mm), Stress (MPa)
E = Young's Modulus or Mod of Elasticity (MPa)
I = 2nd Moment of Area or Area Moment (mm4). Can calculate using SolidEdge sketch. BENDING
[pic]
In our case, we must first convert the mass to Newtons (N). W = kg * 9.81 L is the span length in (mm).
I is the Second Moment of Area in (mm4). We can calculate this for a rectangle using a simple formula; [pic]
For other shapes it is not so simple. We need to calculate these using a program such as Solid Edge (see below).

Determining the value of E in MPa. From the above equation,

Deflection z = W * L3 / (48 * E * I)

so E = W * L3 / (48 * z * I)

Determining Stress in MPa. From the above equation,

Bending Moment (Nmm) M = W*L / 4
and
Maximum Stress (MPa) f = M * y / I
where y = distance from centroid to the bottom (or top) of the beam. This is simply half the depth for all the symmetrical beams except the channel. To find the centroid for the channel you need to use Solid Edge again (same as the Ixx window) [pic]

Laboratory
1. Load another beam onto the rig.
2. Adjust dial gauge to ensure it is touching the beam. Zero the dial face by rotating the lense and locking in place. 3. Apply each load and record the deflection measurement.
4. Check you have all recordings: Beam material, beam cross-sectional dimensions, span length, deflection readings, masses. 5. Make estimates of the errors associated with each measurement. E.g....

...(Set No. 6)
1. Calculate the area A, the location of the neutral axis, and the secondmoment of area (cross section stiffness) IXX for each of the following shapes, and rank them in order of increasing stiffness. Scale the dimensions from the drawings, and work in mm. For a circle,
π r4 I= . 4
X X X (b) (a) X (d)
X X X
X
(c)
X X X X X
X
(e)
(f)
(g)
X
X X
X X
X
(h) (i)
(j)
2
2. A rectangular beam with a cross section 200 mm x 100 mm spans 6 metres and carries a uniform load of 2 kN/m. a) Calculate the reactions. b) Draw the shear force and bendingmoment diagrams. c) Calculate I for the cross section, about the axis of bending. d) Calculate the maximum compressive stress in the beam, and show where it occurs along the length, and on the cross section. e) Calculate the maximum tensile stress in the beam, and show where it occurs along the length, and on the cross section.
2 kN/m
6 metres
3. The machine component shown below can be analysed as an overhung simply supported beam. It is made of cast iron, which is much stronger in compression than in tension. If the maximum stress must be limited to 30 MPa in tension and 100 MPa in compression, calculate the maximum value of the load P that can be applied.
200 50 200
P
50 cross section dimensions in mm 0.5 m
1.0 m
3
4. Calculate the maximum stress in...

...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...

...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
[+]...

...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...

...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...

...simple bending (assumptions)
Material of beam is homogenous and isotropic => constant E in all direction Young’s modulus is constant in compression and tension => to simplify analysis Transverse section which are plane before bending before bending remain plain after bending. => Eliminate effects of strains in other direction (next slide) Beam is initially straight and all longitudinal filaments bend in circular arcs => simplify calculations Radius of curvature is large compared with dimension of cross sections => simplify calculations Each layer of the beam is free to expand or contract => Otherwise they will generate additional internal stresses.
Bending in beams
Key Points: 1. Internal bendingmoment causes beam to deform. 2. For this case, top fibers in compression, bottom in tension.
Bending in beams
Key Points: 1. Neutral surface – no change in length. 2. Neutral Axis – Line of intersection of neutral surface with the transverse section. 3. All cross-sections remain plane and perpendicular to longitudinal axis.
Bending in beams
Key Points: 1. Bendingmoment causes beam to deform. 2. X = longitudinal axis 3. Y = axis of symmetry 4. Neutral surface – does not undergo a change in length
Consider the simply supported beam below:...

...report
“Measurement of bendingmoment and
shear forces for structural analysis”
Azamat Omarov
ID201102658
1.Theory and background
1.1 Summary
That performed laboratory session on bendingmoments and shear forces requires good understanding and sufficient knowledge of axial forces. Bending is defined as a behavior of any structural element that undergoes the external load, which is applied perpendicularly to longitudinal axis. That experiment helps us to find the maximum load that can be applied to the beam with rectangular cross section. Moments are calculated by using statics theory, or multiplying perpendicularly directed load by the respective distance to the pivot point.
1.2 Objective
The main objective of that laboratory is to provide students with basic experience and thus, the comparison between calculated and measured values (software) should be demonstrated to show the ability to apply statics theory from applied mechanics module.
1.3 Theory
Shear forces
The shearing force at any section of a beam is the algebraic sum of the lateral components of the forces acting on either side of the section. F is the resultant reaction on the left of AA. As the beam is in equilibrium then resultant reaction on the right of AA must be downwards.
Figure1. Shear forces diagram
Equilibrium state
∑Fx=0N; ∑Fy=0N; ∑Mo=0N.m (1)
In our case we use AA as a reference...

...LABORATORY EXPERIMENT NO. 3
BENDING OF BEAMS - (a) BendingMoment I
(b) BendingMoment II
SECTION 1
GROUP NUMBER 3
GROUP MEMBERS
1. YEOW SU LEE ( CE085335 )
2. JOUDI J. MOOSOM ( CE085338 )
3. NINI EZLIN ROSLI ( CE086340 )
4. MOHD AFIQ AFIFE BIN ABAS ( CE085310 )
5. ROHAM HADIYOUN ZADEH ( CE085851 )
DATE OF LABORATORY SESSION 6 DECEMBER 2010
DATE OF REPORT SUBMISSION 13 DECEMBER 2010
LAB INSTRUCTOR MISS SITI ALIYYAH MASJUKI
LAB REPORT MARKING |
CRITERIA | Scale |
| Poor | | Acceptable | | Excellent |
A. Appearance, formatting and grammar/spelling | 1 | 2 | 3 | 4 | 5 |
B. Introduction and objective | 1 | 2 | 3 | 4 | 5 |
C. Procedure | 1 | 2 | 3 | 4 | 5 |
D. Results: data, figures, graphs, table, etc. | 1 | 2 | 3 | 4 | 5 |
E. Discussion | 1 | 2 | 3 | 4 | 5 |
F. Conclusions | 1 | 2 | 3 | 4 | 5 |
TABLE OF CONTENT
Section | Page |
Summary | |
Objective | |
Apparatus | |
Procedure | |
Results | |
Discussion | |
Conclusions | |
SUMMARY
When applied loads act along a beam, an internal bendingmoment which varies from point to point along the axis of the beam is developed. A bendingmoment is an internal force that is induced in a restrained structural element when external forces are applied. Failure by...

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