(MT-213L) Mechanics of Materials Lab
Lab Report
Name: Waseem Haider
Roll No. 190992
Class: BEMTS – F-19
Section: A
Instructor: Engr. Nouman
Department of Mechatronics Engineering
Air University, Sector E-9, Islamabad
Experiment No. 12
Objective:
To determine the elastic line of a cantilever beam;
Apparatus:
Beam Apparatus, Steel bar 6 x 20 x 1000 mm, Rider for weight, Suspender for
weights, Weight set, Dial gauge with holder, Support pillar with clamp.
Theory:
The cantilever beam is shown in the figure. In this experiment, the elastic line of a
cantilever beam will be determined and the result will be compared with the result
of the mathematical calculation. The equation for the elastic line of a cantilever bar
loaded with a single force is as follows:
For the Section 0 ≤ x ≤ a
Px2
[3a-x]
v =6EI
For the Section a ≤ x ≤ L
Pa2
[3x-a]
v =6EI
Apparatus Setup:
Procedure:
The experiment is set up as described in the figures. The load remains constant and
is applied at a = 500mm.The deflection of the bar is measured at intervals of 100
mm with the dial gauge. Follow the following steps:
1.
2.
3.
4.
5.
6.
Relieve the bar
Apply the dial gauge at the required position. And set to zero
Load the bar
Read the deflection value and record
Relieve the bar and move the dial gauge to then next position
Repeat the measuring procedure for the remaining readings.
Observations and Calculations:
For a load of F = 10 N where a = 500 mm, the following deflection values are
achieved: Elastic Line of a Cantilever bar can be calculated out as.
Sr.
No.
Length ‘L’
in mm.
1
0
2
100
3
200
4
300
5
400
6
500
7
600
8
700
9
800
Measured
deflection in mm
(VE)
Calculated
deflection in
mm
(VT)
Difference
VT - VE
% Error
Plot:
Draw the graph from the values obtained in the table between the distance from the
support and deflection from calculated and measures values.
Conclusion:
Simulation on SolidWorks
Objective:
The main objective is to simulate the deflection at the point of application of a force
(500 mm) on the cantilever beam by applying load on different distances and is to
compare those results with theoretical and practical forces.
Procedure:
1. Open SolidWorks. Press the sketch icon to draw 2d diagram. In sketch bar
press the rectangle icon and draw a rectangle with dimension 20 x 6 mm.
Fig 12.1: 2d rectangle
2. Press Feature and in Feature tab press Extrude Boss to extrude the
rectangle for 1000 mm to make a rod with dimension 1000 x 20 x 6 mm.
Fig 12.2: Extruded rod
3. To make smaller cuts on the rod for applying external loads, draw a
rectangle on upper face of Rod with dimension 20 x 0.3mm.
Fig 12.3: 2d rectangle on upper face
4. Press linear sketch pattern and set 10 in y direction and 1 in x direction on
the upper face of rod.
Fig 11.4: Linear sketch pattern
5. In Feature tab press Extrude cut and make these 10 rectangles extruded cut
up to 0.01 mm down
Fig 12.5: Extruded cut
6. In upper tool bar press SolidWorks Add Ins.
And then press SolidWorks Simulation and
then press New Study. Confirm static and
click green tick icon.
Fig 12.6: Static Simulation
7. Right click on Fixtures and press Fixed geometry. Select the only 1 sides of
rod and press green tick icon to form fixture at both ends.
Fig 12.7: Fixtures at both sides of rod
8. For applying external loads right click on External load and press force.
Select the rectangle at 0 mm distance and apply 10 N force and click green
tick icon. Also apply gravity from external load.
Fig 12.8: Force at 200 mm
9. To create a mesh right click on mesh and press Create mesh. Select the
whole and press green tick icon. Also assign the material AISI 1020 (Steel
with E = 2 e+11) to rod.
10. Click Run this study and rod will be in deformed position. Repeat the step
8 and apply force at 0 to 800-mm position. Record the results in table and
plot the graphs.
Observations and Results:
1. Force at 0mm position:
F = 10N
Deflection at 500 mm = 5.70 mm
1. Force at 100mm position:
F = 10N
Deflection at 500 mm = 6.02 mm
2. Force at 200mm position:
F = 10N
Deflection at 500 mm = 6.90 mm
3. Force at 300mm position:
F = 10N
Deflection at 500 mm = 8.19 mm
4. Force at 400mm position:
F = 10N
Deflection at 500 mm = 9.76 mm
5. Force at 500mm position:
F = 10N
Deflection at 500 mm = 11.46 mm
6. Force at 600mm position:
F = 10N
Deflection at 500 mm = 13.19 mm
7. At 700mm position:
F = 10N
Deflection at 500 mm = 14.91 mm
8. At 800mm position:
F = 10N
Deflection at 500 mm = 16.64 mm
Comparing all the Deflections
60
Deflection (mm)
50
40
30
20
10
0
0
100
200
300
400
500
600
700
800
Length (mm)
Force at 0 mm
Force at 100 mm
Force at 200 mm
Force at 300 mm
Force at 400 mm
Force at 500 mm
Force at 600 mm
Force at 700 mm
Force at 800 mm
900
1000
For a load of F = 10 N where a = 500 mm, the following deflection values are achieved:
Elastic Line of a Cantilever bar can be calculated out as.
No.
Length ‘L’
in mm.
Measured
deflection at point
(500 mm) in mm
(VE)
1
0
5.70
2
100
6.02
3
200
6.90
4
300
8.19
5
400
9.76
6
500
11.46
7
600
13.19
8
700
14.91
9
800
16.64
Sr.
Conclusion:
Calculated
deflection in
mm
(VT)
Difference
VT - VE
% Error