Comparison of Beam Strength through Finite Element Analysis
Introduction
Three different cases of beams are taken of three different cross-sectional profiles, namely – rectangular, I-section and half I-section. A force of 1500 kN is applied on the smaller face of the beam, uniformly. The length of each beam is 400m. The finite element analysis of each beam are carried out using SolidWorks and the resultant stress, displacement and strain values are obtained for each case. Finally, the best out of the three beams are selected considering the given dimensions and force applied.
Objectives
The objectives of this project are:
- To analyze three cases of prismatic beam for strength
- To find out the values of stress, displacement and strain for each case
- To analyze the strength-to-weight ratio of each beam and select the optimum one
FEA Simulation of Beam: Case 1(Rectangular Section)
Description
In this study a cantilever beam of rectangular cross-section is loaded under a static load and an FEA analysis is carried out to obtain the stress, displacement and strain of the beam.
Assumptions
Beam is :-
- Homogeneous, isotropic and made of Alloy Steel.
- Subjected to test force of 1500 N.
- 400 mm long.
Model Information
|
Dimensions |
Treated As |
Volumetric Properties |
|
Length=400mm Breadth=45mm Depth=80mm |
Solid Body |
Mass:11.088 kg Volume:0.00144 m^3 Density:7700 kg/m^3 Weight:108.662 N
|
Study Properties
|
Study name |
Case 1 |
|
Analysis type |
Static |
|
Mesh type |
Solid Mesh |
|
Thermal Effect: |
On |
|
Thermal option |
Include temperature loads |
|
Zero strain temperature |
298 Kelvin |
|
Include fluid pressure effects from SOLIDWORKS Flow Simulation |
Off |
|
Solver type |
FFEPlus |
|
Inplane Effect: |
Off |
|
Soft Spring: |
Off |
|
Inertial Relief: |
Off |
|
Incompatible bonding options |
Automatic |
|
Large displacement |
Off |
|
Compute free body forces |
On |
|
Friction |
Off |
|
Use Adaptive Method: |
Off |
Units
|
Unit system: |
SI (MKS) |
|
Length/Displacement |
mm |
|
Temperature |
Kelvin |
|
Angular velocity |
Rad/sec |
|
Pressure/Stress |
N/m^2 |
Material Properties
|
Model Reference |
Properties |
||||||||||||||||||||
|
Loads and Fixtures
Fixtures-
|
Fixture name |
Fixture Image |
Fixture Details |
|||||||||||||||
|
Fixed-1 |
|
||||||||||||||||
|
Resultant Forces
|
|||||||||||||||||
Loads-
|
Load name |
Load Image |
Load Details |
||||||
|
Force-1 |
|
Mesh Information
|
Mesh type |
Solid Mesh |
|
Mesher Used: |
Standard mesh |
|
Automatic Transition: |
Off |
|
Include Mesh Auto Loops: |
Off |
|
Jacobian points |
4 Points |
|
Element Size |
11.2949 mm |
|
Tolerance |
0.564745 mm |
|
Mesh Quality Plot |
High |
Mesh Details
|
Total Nodes |
11619 |
|
Total Elements |
7374 |
|
Maximum Aspect Ratio |
3.9167 |
|
% of elements with Aspect Ratio < 3 |
99.9 |
|
% of elements with Aspect Ratio > 10 |
0 |
|
% of distorted elements(Jacobian) |
0 |
|
Time to complete mesh(hh;mm;ss): |
00:00:01 |
Study Results
Stress-
|
Name |
Type |
Min |
Max |
|
Stress1 |
VON: von Mises Stress |
5.256e+02 N/m^2 Node: 8296 |
7.113e+06 N/m^2 Node: 9 |
|
Stress profile for Case 1 (Rectangular Section) |
|||
Displacement-
|
Name |
Type |
Min |
Max |
|
Displacement1 |
URES: Resultant Displacement |
0.000e+00 mm Node: 1 |
3.101e-02 mm Node: 53 |
|
Displacement profile for Case 1 (Rectangular Section) |
|||
Strain-
|
Name |
Type |
Min |
Max |
|
Displacement1 |
URES: Resultant Displacement |
0.000e+00 mm Node: 1 |
3.101e-02 mm Node: 53 |
|
Strain profile for Case 1 (Rectangular Section) |
|||
FEA Simulation of Beam: Case 2(I-Section)
Description
In this study a cantilever beam of I cross-section is loaded under a static load and an FEA analysis is carried out to obtain the stress, displacement and strain of the beam.
Assumptions
Beam is :-
- Homogeneous, isotropic and made of Alloy Steel.
- Subjected to test force of 1500 N.
- 400 mm long.
Model Information
|
Dimensions |
Treated As |
Volumetric Properties |
|
Length=400mm Breadth=40mm Depth=80mm |
Solid Body |
Mass:2.36588 kg Volume:0.000307257 m^3 Density:7700 kg/m^3 Weight:23.1856 N
|
Study Properties
|
Study name |
Case_3_Static_Linear |
|
Analysis type |
Static |
|
Mesh type |
Solid Mesh |
|
Thermal Effect: |
On |
|
Thermal option |
Include temperature loads |
|
Zero strain temperature |
298 Kelvin |
|
Include fluid pressure effects from SOLIDWORKS Flow Simulation |
Off |
|
Solver type |
FFEPlus |
|
Inplane Effect: |
Off |
|
Soft Spring: |
Off |
|
Inertial Relief: |
Off |
|
Incompatible bonding options |
Automatic |
|
Large displacement |
Off |
|
Compute free body forces |
On |
|
Friction |
Off |
|
Use Adaptive Method: |
Off |
Units
|
Unit system: |
SI (MKS) |
|
Length/Displacement |
mm |
|
Temperature |
Kelvin |
|
Angular velocity |
Rad/sec |
|
Pressure/Stress |
N/m^2 |
Material Properties
|
Model Reference |
Properties |
||||||||||||||||||||
|
Loads and Fixtures
Fixtures-
|
Fixture name |
Fixture Image |
Fixture Details |
|||||||||||||||
|
Fixed-1 |
|
||||||||||||||||
|
Resultant Forces
|
|||||||||||||||||
Loads-
|
Load name |
Load Image |
Load Details |
||||||
|
Force-1 |
|
Mesh Information
|
Mesh type |
Solid Mesh |
|
Mesher Used: |
Standard mesh |
|
Automatic Transition: |
Off |
|
Include Mesh Auto Loops: |
Off |
|
Jacobian points |
4 Points |
|
Element Size |
6.86362 mm |
|
Tolerance |
0.343181 mm |
|
Mesh Quality Plot |
High |
Mesh Details
|
Total Nodes |
18125 |
|
Total Elements |
9154 |
|
Maximum Aspect Ratio |
8.9698 |
|
% of elements with Aspect Ratio < 3 |
87.2 |
|
% of elements with Aspect Ratio > 10 |
0 |
|
% of distorted elements(Jacobian) |
0 |
|
Time to complete mesh(hh;mm;ss): |
00:00:02 |
Study Results
Stress-
|
Name |
Type |
Min |
Max |
|
Stress1 |
VON: von Mises Stress |
1.794e+03 N/m^2 Node: 62 |
2.084e+07 N/m^2 Node: 1082 |
|
Stress profile for Case2(I-Section) |
|||
Displacement-
|
Name |
Type |
Min |
Max |
|
Displacement1 |
URES: Resultant Displacement |
0.000e+00 mm Node: 1 |
8.550e-02 mm Node: 1141 |
|
Stress profile for Case2(I-Section) |
|||
Strain-
|
Name |
Type |
Min |
Max |
|
Strain1 |
ESTRN: Equivalent Strain |
9.235e-09 Element: 212 |
7.609e-05 Element: 7788 |
|
Stress profile for Case2(I-Section) |
|||
FEA Simulation of Beam: Case 3(Half I-Section)
Description
In this study a cantilever beam of half-I cross-section is loaded under a static load and an FEA analysis is carried out to obtain the stress, displacement and strain of the beam.
Assumptions
Beam is :-
- Homogeneous, isotropic and made of Alloy Steel.
- Subjected to test force of 1500 N.
- 400 mm long.
Model Information
|
Dimensions |
Treated As |
Volumetric Properties |
|
Length=400mm Breadth=45mm Depth=80mm |
Solid Body |
Mass:3.22947 kg Volume:0.000419412 m^3 Density:7700 kg/m^3 Weight:31.6488 N
|
Study Properties
|
Study name |
Beam_3_Static |
|
Analysis type |
Static |
|
Mesh type |
Solid Mesh |
|
Thermal Effect: |
On |
|
Thermal option |
Include temperature loads |
|
Zero strain temperature |
298 Kelvin |
|
Include fluid pressure effects from SOLIDWORKS Flow Simulation |
Off |
|
Solver type |
FFEPlus |
|
Inplane Effect: |
Off |
|
Soft Spring: |
Off |
|
Inertial Relief: |
Off |
|
Incompatible bonding options |
Automatic |
|
Large displacement |
Off |
|
Compute free body forces |
On |
|
Friction |
Off |
|
Use Adaptive Method: |
Off |
Units
|
Unit system: |
SI (MKS) |
|
Length/Displacement |
mm |
|
Temperature |
Kelvin |
|
Angular velocity |
Rad/sec |
|
Pressure/Stress |
N/m^2 |
Material Properties
|
Model Reference |
Properties |
||||||||||||||||||||
|
Loads and Fixtures
Fixtures-
|
Fixture name |
Fixture Image |
Fixture Details |
|||||||||||||||
|
Fixed-1 |
|
||||||||||||||||
|
Resultant Forces
|
|||||||||||||||||
Loads-
|
Load name |
Load Image |
Load Details |
||||||
|
Force-1 |
|
Mesh Information
|
Mesh type |
Solid Mesh |
|
Mesher Used: |
Standard mesh |
|
Automatic Transition: |
Off |
|
Include Mesh Auto Loops: |
Off |
|
Jacobian points |
4 Points |
|
Element Size |
7.48731 mm |
|
Tolerance |
0.374366 mm |
|
Mesh Quality Plot |
High |
Mesh Details
|
Total Nodes |
16375 |
|
Total Elements |
8473 |
|
Maximum Aspect Ratio |
8.8148 |
|
% of elements with Aspect Ratio < 3 |
95.5 |
|
% of elements with Aspect Ratio > 10 |
0 |
|
% of distorted elements(Jacobian) |
0 |
|
Time to complete mesh(hh;mm;ss): |
00:00:01 |
Study Results
Stress-
|
Name |
Type |
Min |
Max |
|
Stress1 |
VON: von Mises Stress |
6.499e+04 N/m^2 Node: 6609 |
3.841e+07 N/m^2 Node: 16374 |
|
Stress profile for Beam 3(Half I-Section) |
|||
Displacement-
|
Name |
Type |
Min |
Max |
|
Displacement1 |
URES: Resultant Displacement |
0.000e+00 mm Node: 1 |
3.018e-01 mm Node: 61 |
|
Stress profile for Beam 3(Half I-Section) |
|||
Strain-
|
Name |
Type |
Min |
Max |
|
Strain1 |
ESTRN: Equivalent Strain |
2.245e-07 Element: 7763 |
1.277e-04 Element: 7913 |
|
Stress profile for Beam 3(Half I-Section) |
|||
Results
The results obtained from above analyses are tabulated below:-
|
Case No. |
Maximum Stress(Pa) |
Maximum Displacement(µm) |
Maximum Strain(µm) |
Mass (kg) |
Strength-to-Weight Ratio(SWR)* |
|
1 (Rectangular) |
7.113x106 |
31.01 |
2.640x10-5 |
11.0880 |
6.4123x105 |
|
2(I-section) |
2.084x107 |
85.50 |
7.609x10-5 |
2.3659 |
8.8084x106 |
|
3(Half I-section) |
3.841x107 |
303.80 |
1.668x10-4 |
3.2295 |
1.1893x107 |
*SWR=Maximum Stress/Mass
Discussion
Comprehensive Results for Case 1(Rectangular Section)
Comprehensive Results for Case 2(I-Section)
Comprehensive Results for Case 3(Half I-Section)
In the results table, a new parameter, namely “Strength-to-Weight Ratio” or “SWR” is introduced. This parameter was subsequently defined as the ratio of the maximum stress experienced to the mass of the beam. Physically, this ratio signifies how much of the load is borne per unit mass of the beam. Since, in all cases stresses produced by the load of 1500N are well within the yield strength, we will try to maximize the optimization of material by selecting a beam with lesser mass. Consequently, we will have a lighter beam that will decrease the overall weight of the structure or machine.
Conclusion
From the results part, it is observed that the Strength to Weight ratio of beam in Case 3 is highest. However, Case 2 is lighter than Case 3. As our factors of optimization are Strength-to-Weight Ratio (SWR) and Mass, we arrive at the conclusion that Case 2,i.e., I-section is the most optimized design in this case as it is the lightest of all beams and yet has the second highest SWR. Thus, Case 2 or I-section is recommended out of the three beams as it is objectively the best out of the three beams considering optimization parameters.