Comparison of Beams in Bending Load using SolidWorks

OBJECTIVE:

To compare performance of beam with different cross-section under bending load. The different cross sectional beams under study are:

• Rectangular Cross Sectional Beam
• I Cross-Sectional Beam
• C Cross-Sectional Beam

Static Analysis of Beam under Bending Load-

3 D Static Analysis was performed for three different cross sectional cantilever beams

under uniformly distributed load using Finite Element Method.

Case 1: Rectangular Cross Sectional Beam

GEOMETRY MODEL:

The beam was extruded to 400 mm length & the cross-section was made as

mentioned in the challenge.

Mass:11.088 kg

Volume:0.00144 m^3

Density:7700 kg/m^3

Weight:108.662 N

MATERIAL CONDITION:

Alloy Steel (Yield Strength = 620.42 MPa) was applied as a material to the beam.

Linear Elastic Isentropic was slected as a material model.

Model Reference	Properties	Components
	Name: Alloy Steel Model type: Linear Elastic Isotropic Default failure criterion: Max von Mises Stress Yield strength: 6.20422e+08 N/m^2 Tensile strength: 7.23826e+08 N/m^2 Elastic modulus: 2.1e+11 N/m^2 Poisson's ratio: 0.28 Mass density: 7700 kg/m^3 Shear modulus: 7.9e+10 N/m^2 Thermal expansion coefficient: 1.3e-05 /Kelvin	SolidBody 1(Boss-Extrude1)(Rect_Beam)

BOUNDRY CONDITION:

One end face of the beam was made fixed to behave it as a cantilever beam.

Face 1 with dimensions 45mm X 80mm was made fixed.

Fixture name	Fixture Image	Fixture Details
Fixed-1		Entities: 1 face(s) Type: Fixed Geometry
Resultant Forces Components X Y Z Resultant Reaction force(N) -0.0163002 1500.01 -0.0123444 1500.01 Reaction Moment(N.m) 0 0 0 0

LOAD CONDITION:

Uniformly Distributed Load (UDL) of 1500 Newton was applied on upper face

(dimensions 45mm X 400mm) perpendicular to the fixed plane.

Load name	Load Image	Load Details
Force-1		Entities: 1 face(s) Type: Apply normal force Value: 1500 N

MESH PARAMETER:

The beam was refined with standard triangular mesh of size 6 mm.

RESULT:

The result consists of 3 plots - Stress Plot, Displacement Plot & Strain Plot.

The minimum factor of safety is 66.

The mass of the beam is 11.088kg.

Name	Type	Min	Max
Stress1	VON: von Mises Stress	0.000 N/mm^2 (MPa) Node: 1495	9.448 N/mm^2 (MPa) Node: 96

The maximum stress produced is less than the yield strength which indicates safe loading.

Name	Type	Min	Max
Displacement1	URES: Resultant Displacement	0.000 mm Node: 82	0.031 mm Node: 15

Name	Type	Min	Max
Strain1	ESTRN: Equivalent Strain	7.257e-10 Element: 19589	2.987e-05 Element: 7564

Case 2: I Cross-Sectional Beam

GEOMETRY MODEL:

The beam was extruded to 400 mm length & the cross-section was made as

mentioned in the challenge.

Mass:2.36367 kg

Volume:0.000306969 m^3

Density:7700 kg/m^3

Weight:23.1639 N

MATERIAL CONDITION:

Alloy Steel (Yield Strength = 620.42 MPa) was applied as a material to the beam.

Linear Elastic Isentropic was slected as a material model.

Model Reference	Properties	Components
	Name: Alloy Steel Model type: Linear Elastic Isotropic Default failure criterion: Max von Mises Stress Yield strength: 6.20422e+08 N/m^2 Tensile strength: 7.23826e+08 N/m^2 Elastic modulus: 2.1e+11 N/m^2 Poisson's ratio: 0.28 Mass density: 7700 kg/m^3 Shear modulus: 7.9e+10 N/m^2 Thermal expansion coefficient: 1.3e-05 /Kelvin	SolidBody 1(Boss-Extrude1)(I Beam)

BOUNDRY CONDITION:

One end face of the beam was made fixed to behave it as a cantilever beam.

Face 1 with dimensions 45mm X 80mm was made fixed.

Fixture name	Fixture Image	Fixture Details
Fixed-1		Entities: 1 face(s) Type: Fixed Geometry
Resultant Forces Components X Y Z Resultant Reaction force(N) -0.683352 1499.96 -0.000821114 1499.96 Reaction Moment(N.m) 0 0 0 0

LOAD CONDITION:

Uniformly Distributed Load (UDL) of 1500 Newton was applied on upper face

(dimensions 40mm X 400mm) perpendicular to the fixed plane.

Load name	Load Image	Load Details
Force-1		Entities: 1 face(s) Type: Apply normal force Value: 1500 N

MESH PARAMETER:

The beam was refined with standard triangular mesh of size 6 mm.

RESULT:

The result consists of 3 plots - Stress Plot, Displacement Plot & Strain Plot.

Name	Type	Min	Max
Stress1	VON: von Mises Stress	0.002 N/mm^2 (MPa) Node: 15173	23.174 N/mm^2 (MPa) Node: 3058

The maximum stress produced is less than the yield strength which indicates safe loading.

Name	Type	Min	Max
Displacement1	URES: Resultant Displacement	0.000 mm Node: 70	0.086 mm Node: 2991

Name	Type	Min	Max
Strain1	ESTRN: Equivalent Strain	8.722e-09 Element: 1391	7.668e-05 Element: 10671

The minimum factor of safety is 27.

The mass of the beam is 2.363kg.

Case 3: C Cross-Sectional Beam

GEOMETRY MODEL:

The beam was extruded to 400 mm length & the cross-section was made as

mentioned in the challenge.

Mass:3.2225 kg

Volume:0.000418506 m^3

Density:7700 kg/m^3

Weight:31.5805 N

MATERIAL CONDITION:

Alloy Steel (Yield Strength = 620.42 MPa) was applied as a material to the beam.

Linear Elastic Isentropic was slected as a material model.

Model Reference	Properties	Components
	Name: Alloy Steel Model type: Linear Elastic Isotropic Default failure criterion: Max von Mises Stress Yield strength: 6.20422e+08 N/m^2 Tensile strength: 7.23826e+08 N/m^2 Elastic modulus: 2.1e+11 N/m^2 Poisson's ratio: 0.28 Mass density: 7700 kg/m^3 Shear modulus: 7.9e+10 N/m^2 Thermal expansion coefficient: 1.3e-05 /Kelvin	SolidBody 1(Boss-Extrude1)(U_Beam)
Curve Data:N/A

BOUNDRY CONDITION:

One end face of the beam was made fixed to behave it as a cantilever beam.

Face 1 with C cross-section was made fixed.

Fixture name	Fixture Image	Fixture Details
Fixed-1		Entities: 1 face(s) Type: Fixed Geometry
Resultant Forces Components X Y Z Resultant Reaction force(N) -1499.96 -0.00524139 0.0839424 1499.96 Reaction Moment(N.m) 0 0 0 0

LOAD CONDITION:

Uniformly Distributed Load (UDL) of 1500 Newton was applied on upper face

(dimensions 45mm X 400mm) perpendicular to the fixed plane.

Load name	Load Image	Load Details
Force-1		Entities: 1 face(s) Type: Apply normal force Value: 1500 N

MESH PARAMETER:

The beam was refined with standard triangular mesh of size 6 mm.

RESULT:

The result consists of 3 plots - Stress Plot, Displacement Plot & Strain Plot.

Name	Type	Min	Max
Stress1	VON: von Mises Stress	0.063 N/mm^2 (MPa) Node: 18240	39.833 N/mm^2 (MPa) Node: 27502

The maximum stress produced is less than the yield strength which indicates safe loading.

Name	Type	Min	Max
Displacement1	URES: Resultant Displacement	0.000 mm Node: 70	0.304 mm Node: 139

Name	Type	Min	Max
Strain1	ESTRN: Equivalent Strain	2.651e-07 Element: 6860	1.405e-04 Element: 12922

The minimum factor of safety is 16.

The mass of the beam is 3.225kg.

OVERALL RESULT:

Sr. No. Property Rectangular Beam I Beam C Beam

1. Max. Stress (MPa) 9.448 23.174 39.833

2. Max. Displacement (mm) 0.031 0.086 0.304

3. Max. Strain 2.987e-05 7.668e-05 1.405e-04

4. Mass (kg) 11.088 2.363 3.225

5. Factor of Safety 66 27 16

From the above table, it can clearly be observed that in comparison with the other two beams; in the rectangular beam the developed stress is the least with least displacement & least strain but with maximum factor of safety, it has a major drawback i.e. maximum weight. More weight means more cost.

In comparison with the other two beams, the I beam develops average value of stress, displacement, strain & factor of safety but with the least value of weight. Least weight means least cost.

In comparison with the other two beams, the C beam develops maximum value of stress, displacement & strain but with least factor of safety & average value of weight.

So a conclusion can be made in the favour of I Beam. Since, having the least weight makes it much more economical and a factor of safety of 27, allows a good range of stresses to be handled by the beam. The rectangular beam failed due to its excessive mass and the C beam failed due to its leasgt factor of safety & maximum displacement.

CONCLUSION:

The best & most economical beam is I cross-section beam.