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ME 2356 Laboratory Template
1
Department of Mechanical and Industrial Engineering
ME 2356: Laboratory for Mechanics of Materials
Bending Test
Submitted by
Sydney Rodriguez
Date Submitted: 11/30/23
Date Performed: 11/9/23
Lab Section: 12
Lab TA: Lindsey Young
Course Instructor: Marguerite Matherne
ME 2356 Laboratory Template
2
1.
Introduction
This experiment explores how beams bend under various loads and introduces column buckling
due to compression. It covers three-point bending, comparing calculated and measured
deflections, and examines how extra supports affect beam deflection. The critical buckling load
for columns under different support conditions is also studied. The aim is to understand beam
behavior and the abrupt loss of stability in columns under compression.
2.
Methods and results
2.1
Instron
Procedure
A material sample, with measured width and thickness and a set length of 110mm, was tested
using an Instron machine. The upper jaw was lowered until it lightly touched the sample, set on
two support bars. Bluehill software was utilized to set up a compression method with metric
units, a test rate of 10 mm/min, and the selection of raw data for measurement. The test was
initiated, monitoring the curve until it departed from linearity (usually after 10-15mm of
deflection) and then stopped. Following the test, the specimen was removed from the machine
and placed on a flat surface to observe any plastic deformation.
Shear force diagram and Bending moment diagram including the maximum value of the
bending moment (M
max
) in terms of P and L.
ME 2356 Laboratory Template
3
Results
Sample material and measurements table
Table 1. Steel data.
Parameter
Initial value (mm)
Length
200
Thickness
9.49
Width
25.41
Second moment of area, I
1.8098e03 (mm^4)
Load vs. deflection plot for the predicted and experimental data
Yield strength
The yield strength, σy, at the given triangle is about 2092.57 N/mm.
The location where the beam starts to yield
The point at which yielding appears first is (3.3738, 6960.6) (where the line starts to
curve).
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ME 2356 Laboratory Template
4
Discussion
Answer any question from instruction under section “Instron: results, analysis, and
reporting” (#6 and 7)
The calculated values of the Youngs Modulus range from 170000 to 200000 MPa.
This is close to the predicted values ranging from 190000 to 230000 found online.
The results are extremely close and may be a bit off due to human error. If others
were to repeat this experiment, they should expect similar results.
ME 2356 Laboratory Template
5
2.2
Beam deflection
Procedure
In the outlined experimental procedure, steel beams with specified dimensions—20mm in width
and 3.25mm in thickness—were subjected to deflection and load distribution tests. The
experiment began with the calibration of the measuring instruments. Load cells and dial gauges
were set to zero to negate any initial readings that could skew the results. The beams were then
placed on supports, the positions of which were determined as per the accompanying diagram. A
weight hanger, applying a force of 2.5 N, was positioned at the designated point on the beam to
simulate a point load. Subsequent measurements of the beam's deflection were taken at points C
and D using the dial gauges, which are designed to measure small displacements with high
precision. Concurrently, load cells recorded the reaction forces at the beam's supports. This was
repeated for a beam that is indeterminate and determinant.
Results
Deflection and support forces (and moments where available)
Table 2. Beam deflection data.
Discussion
Answer any question from instruction under section “Beam deflection: results, analysis,
and reporting” (#3 and #4)
o
The beam with the larger deflection is the simply supported or determinate one.
This is due to an extra acting moment.
o
The calculated and experiment values are far off but this is most likely due to the
beam being slightly different or calculation errors. If someone repeated this
experiment, they would achieve closer results toward the calculated values.
Point
Problem 1: simple support end
Problem 2: overhang end
Experiment value
Calculate value
Experiment value
Calculate value
Force @ A
-1.08
1.40625
-1.53
-2.109
Moment @ A
N/A
N/A
N/A
0.00574
Force @ B
3.75
3.90625
4.03
4.609
Deflection @ C
-6.50
0.00053
-6.72
-0.0126
Deflection @ D
1.39
8.22
0.99
0.05589
ME 2356 Laboratory Template
6
2.3
Buckling
Procedure
The experiment was designed to observe the effects of compressive forces on steel beams with
predefined dimensions of 600mm in length, 20mm in width, and 4mm in thickness. The
procedure was initiated by setting all instruments measuring load to zero to ensure accuracy.
Following this, a crank mechanism was employed to exert a compressive load upon the beam.
The crank was turned to the right gradually until a noticeable deformation in the beam's shape
was observed, or until the force readings stabilized or altered minimally, indicating the load limit
of the beam. This was repeated for a pin-pin supported beam and a pin-clamp supported beam.
Results
Prediction of critical buckling forces from equations.
Be sure to show the values of
effective length factor that you use.
Table 1. Beam deflection experimental data.
pin-pin support
pin-clamp support
Experiment value
Calculate value
Experiment value
Calculate value
Experimental critical force
511
350.92
1076
501.31
Discussion
Answer any question from instruction under section “Buckling: results, analysis, and
reporting” (#3, 4, 5)
o
If both ends had fixed supports, the beam’s critical force would increase.
o
Some error could be due to the setup of the experiment and the use of a
hypothetical Youngs Modulus value. If others repeated this experiment, they
would hopefully get closer values to the calculated one.
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ME 2356 Laboratory Template
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Appendix:
MATLAB code
% Isotron sample
%clear data
clearvars;
clc;
%read file
filename =
'lab3test.csv'
;
T = readmatrix(filename);
%conversions
time = T(:,2);
displacement = T(:,3);
force = T(:,4)*1000;
%sample properties (mm)
b = 25.41;
h = 9.49;
L = 200;
% calculations
I = (b * (h^3))/12;
M = force*L/I;
yield = M/I;
% Young's Modulus (E)
E = (force./displacement).*(L^3/(48*I));
E1= 190000;
% Predicted values
predicted = force.* L^3 ./ (48 .* I .* E1);
bending = force./displacement;
%plot load vs deflection
figure(1)
plot(displacement, force);
hold
on
plot(predicted, force);
hold
on
title(
'Load vs Deflection'
);
xlabel(
'Deflection (mm)'
);
ylabel(
'Force (N)'
);
Related Questions
I Review
Learning Goal:
Part A- Vertical impact
To calculate displacement and stresses due to vertical and horizontal impact loads.
A 10-kg block is dropped from 1.5 m onto the center of a simply supported beam with a length 3 m. The beam has a square section with side length 6.5 cm. The material has E = 200 GPa . What is the maximum
deflection?
When an object strikes a structure that responds by deforming in linear elastic fashion, the
object comes to rest when the structure has undergone maximum deflection. At that
moment, the structure's strain energy must equal the sum of the energies before the impact,
including both the object's kinetic energy and its gravitational potential energy.
Express your answer with appropriate units to three significant figures.
> View Available Hint(s)
When an object falls from rest onto a structure, the object's gravitational potential energy is
converted into strain energy in the structure. The total strain energy in the structure at the
point of…
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Needs Complete typed solution with 100 % accuracy.
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Please show work
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Question 2
You are a biomedical engineer working for a small orthopaedic firm that fabricates rectangular shaped fracture
fixation plates from titanium alloy (model = "Ti Fix-It") materials. A recent clinical report documents some problems with the plates
implanted into fractured limbs. Specifically, some plates have become permanently bent while patients are in rehab and doing partial
weight bearing activities.
Your boss asks you to review the technical report that was generated by the previous test engineer (whose job you now have!) and used to
verify the design. The brief report states the following... "Ti Fix-It plates were manufactured from Ti-6Al-4V (grade 5) and machined into
solid 150 mm long beams with a 4 mm thick and 15 mm wide cross section. Each Ti Fix-It plate was loaded in equilibrium in a 4-point bending
test (set-up configuration is provided in drawing below), with an applied load of 1000N. The maximum stress in this set-up was less than the
yield stress for the…
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Please show work for practice problem 12
arrow_forward
calculate the theoretical stress using the flexure or bending stress formula. The experimental se
is shown in Figure 1:
•
L
LB 10 inches
w = 1.5 inches
t = 0.25 inches
LB
Take a few minutes to solve the following pre-lab exercise problems before continuing with the
background unit:
Problem 1:
An experiment was set up according to Figure 1 with the following:
L=12 inches
Figure 1: Simple cantilever beam
with single longitudinal strain gage
Search
t
P = 4 lbs
With the load applied, the longitudinal strain gage reading was recorded as 83 us
(microstrain). Determine the elastic modulus of the beam material. What material is it?
MEXY
arrow_forward
of the Origin. Overall drafting standard -
Create the illustrated part. Note the location
1.50
1.25
ANSI.
Calculate the overall mass of the
illustrated model. Apply the Mass
Properties tool.
Think about the steps that you would
take to build the model.
2.25
Given:
A = 3.50
B= 70
Material: 1060 Alloy
Density = 0.0975 Ib/in^3
Units: IPS
Decimal places = 2
Review the provided information
carefully.
Units are represented in the IPS (inch, pound, second)
system.
A = 3.50in, B = .70in
bliud of s
Origin
PAGE 2-95
Eniter
insert
Cut
arrow_forward
Learning Goal:
To use Mohr's circle to determine the principal stresses, the maximum in-plane shear stress, and the average normal stress in an element.
The state of plane stress on an element is shown below. Let oz= 30.0 MPa, O, = -100.0 MPa, and Try = 50.0 MPa
100 MPa
50.0 MPa
30.0 MPa
Part A - Construction of Mohr's circle for the state of stress
For the element shown, construct Mohr's circle for the state of stress shown associated with the x plane.
First, select the center of Mohr's circle (point C) and select the point that represents the state of plane stress shown (point A). Given these two points, determine the length of the line connecting these two points, which represents the radius R of the Mohr's
circle.
arrow_forward
Please give the detailed solution.
Don't use chatgpt for this question.
Thanks
arrow_forward
1.
1100
A.
30%
B.
1.1 m
1.0 m
A
F= 255 N
0.5 m
1.5 m
DGB
WARNING! The figure is not drawn to scale. For the force in the chain CB, ca
IMAGES NOTES DISCUSS UNITS STATS HELP
PREFERENCES
Part Description
the magnitude of component
parallel to the hinge axis of the
door,
(include units with answer)
0.5 m
Answer
118.77 N
Format Check
the magnitude of the component
parallel to the edge of the door that 218.17 N
is perpendicular to the hinge axis,
(include units with answer)
Format Check
Save
25 pts.7 75%
5% try penalty
31.67 pts.95%
5% try penalty
Status
Tr
● W
#tries:
**
Tr
• W.
#tries:
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I need correct solution only handwritten listen again only handwritten
arrow_forward
Learning Goal:
To use Hooke's law to determine the value of an axial load applied to a rectangular
shape and to determine its lateral expansion.
The element shown below is subjected to the axial compressive force P, which
causes the shape to contract longitudinally in the direction a distance of
8 = 0.720 mm. Let h = 144.5 mm, w = 88.50 mm, and L = 298.0 mm. Assume
the element is made from steel that has a modulus of elasticity of E= 200 GPa and
a value of Poisson's ratio of v=0.32.
♥ Part A Value of the axial load
Determine the value of the axial load P.
Express your answer to four significant figures and include the appropriate
units.
View Available Hint(s)
P =
Submit
P
μÀ
Value
Units
?
Part B Lateral expansion in the y direction
Determine the lateral expansion in the y direction due to the axial load.
Express your answer to four significant figures and include the appropriate
units.
View Available Hint(s)
dy =
Submit
d₂ =
Value
Part C - Lateral expansion in the z direction
μA
Submit…
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You are a structural Engineer who works in Dar Al Handasah company. Your manager has
called for a meeting and provided you with the below schematic design of a concrete beam that
might be implemented at one of the sites. You were requested to calculate the
following: (make 15 KN bold)
40
KN
15
KN
20
KN
45
30
KN
40
KN
16
20
Figure 1: Concrete Beam
1. Find the equivalent forces of the disturbed loads.
2. Sketch the beam showing all the applied forces (reaction and equivalent
forces) and allocate them into their suitable locations proper points.
3. Apply the moment equations in the equilibrium state to find the value of the reaction
forces at points A and B.
4. If the given beam in Figure 1 compressed shrank to be 19.98 meter where the
original temperature was at the given temperature T1=200 K, find the
temperature (T2) after the compression shrinking.
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Kindly do not re-submit your answers if you have solved the problems in this post. I post multiple questions of the same type to get an idea from other tutors. Thank you, Tutor! S.2
Statics of Rigid Bodies
Content Covered:
- Method of Sections
Direction: Create 1 problem based on the topic "Method of Sections" and then solve them with a complete solution. In return, I will give you a good rating. Thank you so much!
Note: Please bear in mind to create 1 problem based on the topic "Method of Sections." Be careful with the calculations in the problem. Kindly double check the solution and answer if there is a deficiency. And also, box the final answer. Thank you so much!
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For my assigment, I was asked to design a electric motorbike that has a peformance equal to Honda CBR1000 Fireblade which has a petrol engine. A part of the the assignment is to calculate " An estimate of maximum Power your new motor will need to generate to match the Honda’s performance." I can make the assumption, apart from changing the motor, everything else is going to stay the same so the fairing,the rider and etc they're gonna be the same for the two bikes. So can you please tell me how I can calculate that which information would I need ?
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A long steel rod is placed horizontally between two supports, one at each end. The rod bends a little in the center. Which property of this rod can be used to estimate how much the rod should bend at the center?
1.
Its Shear Modulus
2.
Its Young's Modulus
3.
All of these Moduli can be used to compute how much it bends.
4.
Its Bulk Modulus.
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Fixed/built-in or encastré beams are usually used in structure due to their high stability and performance in
resisting shear stress and bending moment. Your role in building and construction company is to analyse the
shear force and bending moment in order to provide better design of such beams under variety of loads. Your
manager asked you to provide a complete analysis as well as to deliver a report including your design
recommendations.
100 KN/m
150 kN
z (m)
5
7
10
Figure.2: Encastré beam under variety of loads
Your tasks are as follows:
1- Construct free-body diagram (FBD) to show the reaction forces and moments, equivalent force of the
distributed load., knowing that the upward reaction force on left side is 250 kN and the reaction moment
is clockwise with a value of 1500 kN.m.
2- Show FBD for each required section/cutting, include the internal forces and moments.
3- Write the distribution functions of the shear force and bending moment for each cut in the beam.
4- By hand…
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HOMEWORK
Engineering Materials
1. Consider a cylindrical specimen of some hypothetical metal alloy that has a diameter of 10.0 mm.
A tensile force of 1500 N produces an elastic reduction in diameter of 6.7 x 10 mm. Compute the
elastic modulus of this alloy, given that Poisson's ratio is 0.35.
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Related Questions
- I Review Learning Goal: Part A- Vertical impact To calculate displacement and stresses due to vertical and horizontal impact loads. A 10-kg block is dropped from 1.5 m onto the center of a simply supported beam with a length 3 m. The beam has a square section with side length 6.5 cm. The material has E = 200 GPa . What is the maximum deflection? When an object strikes a structure that responds by deforming in linear elastic fashion, the object comes to rest when the structure has undergone maximum deflection. At that moment, the structure's strain energy must equal the sum of the energies before the impact, including both the object's kinetic energy and its gravitational potential energy. Express your answer with appropriate units to three significant figures. > View Available Hint(s) When an object falls from rest onto a structure, the object's gravitational potential energy is converted into strain energy in the structure. The total strain energy in the structure at the point of…arrow_forwardNeeds Complete typed solution with 100 % accuracy.arrow_forwardPlease show workarrow_forward
- Question 2 You are a biomedical engineer working for a small orthopaedic firm that fabricates rectangular shaped fracture fixation plates from titanium alloy (model = "Ti Fix-It") materials. A recent clinical report documents some problems with the plates implanted into fractured limbs. Specifically, some plates have become permanently bent while patients are in rehab and doing partial weight bearing activities. Your boss asks you to review the technical report that was generated by the previous test engineer (whose job you now have!) and used to verify the design. The brief report states the following... "Ti Fix-It plates were manufactured from Ti-6Al-4V (grade 5) and machined into solid 150 mm long beams with a 4 mm thick and 15 mm wide cross section. Each Ti Fix-It plate was loaded in equilibrium in a 4-point bending test (set-up configuration is provided in drawing below), with an applied load of 1000N. The maximum stress in this set-up was less than the yield stress for the…arrow_forwardPlease show work for practice problem 12arrow_forwardcalculate the theoretical stress using the flexure or bending stress formula. The experimental se is shown in Figure 1: • L LB 10 inches w = 1.5 inches t = 0.25 inches LB Take a few minutes to solve the following pre-lab exercise problems before continuing with the background unit: Problem 1: An experiment was set up according to Figure 1 with the following: L=12 inches Figure 1: Simple cantilever beam with single longitudinal strain gage Search t P = 4 lbs With the load applied, the longitudinal strain gage reading was recorded as 83 us (microstrain). Determine the elastic modulus of the beam material. What material is it? MEXYarrow_forward
- of the Origin. Overall drafting standard - Create the illustrated part. Note the location 1.50 1.25 ANSI. Calculate the overall mass of the illustrated model. Apply the Mass Properties tool. Think about the steps that you would take to build the model. 2.25 Given: A = 3.50 B= 70 Material: 1060 Alloy Density = 0.0975 Ib/in^3 Units: IPS Decimal places = 2 Review the provided information carefully. Units are represented in the IPS (inch, pound, second) system. A = 3.50in, B = .70in bliud of s Origin PAGE 2-95 Eniter insert Cutarrow_forwardLearning Goal: To use Mohr's circle to determine the principal stresses, the maximum in-plane shear stress, and the average normal stress in an element. The state of plane stress on an element is shown below. Let oz= 30.0 MPa, O, = -100.0 MPa, and Try = 50.0 MPa 100 MPa 50.0 MPa 30.0 MPa Part A - Construction of Mohr's circle for the state of stress For the element shown, construct Mohr's circle for the state of stress shown associated with the x plane. First, select the center of Mohr's circle (point C) and select the point that represents the state of plane stress shown (point A). Given these two points, determine the length of the line connecting these two points, which represents the radius R of the Mohr's circle.arrow_forwardPlease give the detailed solution. Don't use chatgpt for this question. Thanksarrow_forward
- 1. 1100 A. 30% B. 1.1 m 1.0 m A F= 255 N 0.5 m 1.5 m DGB WARNING! The figure is not drawn to scale. For the force in the chain CB, ca IMAGES NOTES DISCUSS UNITS STATS HELP PREFERENCES Part Description the magnitude of component parallel to the hinge axis of the door, (include units with answer) 0.5 m Answer 118.77 N Format Check the magnitude of the component parallel to the edge of the door that 218.17 N is perpendicular to the hinge axis, (include units with answer) Format Check Save 25 pts.7 75% 5% try penalty 31.67 pts.95% 5% try penalty Status Tr ● W #tries: ** Tr • W. #tries:arrow_forwardI need correct solution only handwritten listen again only handwrittenarrow_forwardLearning Goal: To use Hooke's law to determine the value of an axial load applied to a rectangular shape and to determine its lateral expansion. The element shown below is subjected to the axial compressive force P, which causes the shape to contract longitudinally in the direction a distance of 8 = 0.720 mm. Let h = 144.5 mm, w = 88.50 mm, and L = 298.0 mm. Assume the element is made from steel that has a modulus of elasticity of E= 200 GPa and a value of Poisson's ratio of v=0.32. ♥ Part A Value of the axial load Determine the value of the axial load P. Express your answer to four significant figures and include the appropriate units. View Available Hint(s) P = Submit P μÀ Value Units ? Part B Lateral expansion in the y direction Determine the lateral expansion in the y direction due to the axial load. Express your answer to four significant figures and include the appropriate units. View Available Hint(s) dy = Submit d₂ = Value Part C - Lateral expansion in the z direction μA Submit…arrow_forward
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