Comparison of bending in beams in Solidworks

AIM : To compare the performance of three types of beams under a bending load.

OBJECTIVES :

1. To design 3D models of beams according to given dimensions.
2. To run a static simulation for the three Cantilever beams with boundary conditions as,

• Apply a load of 1500N on the smaller face(i.e. 45mm face for case 1, 40mm face for case 2 and 45 mm face for case 3) and compare the results of stress, displacement and strain for all the three cases and suggest the best out of the three.

INTRODUCTION : A beam is a structural member whose length along one direction, called the longitudinal axis, is larger than its dimensions on the plane perpendicular to it and is subjected to only transverse loads (i.e., the loads acting perpendicular to the longitudinal axis). A typical beam with rectangular cross section is shown in figure .Thus, this beam occupies the points in the Euclidean point space defined by B = {(x,y,z)|- l ≤ x ≤ l,-c ≤ y ≤ c,-b ≤ z ≤ b} where l, c and b are constants, such that l > c ≥ b with l∕c typically in the range 10 to 20.

Beams can be classified into many types based on three main criteria. They are as follows:

• Based on geometry:

1. Straight beam – Beam with straight profile
2. Curved beam – Beam with curved profile
3. Tapered beam – Beam with tapered cross section
4. Based on the shape of cross section:
5. I-beam – Beam with ‘I’ cross section
6. T-beam – Beam with ‘T’ cross section
7. C-beam – Beam with ‘C’ cross section

• Based on equilibrium conditions:

1. Statically determinate beam – For a statically determinate beam, equilibrium conditions alone can be used to solve reactions.
2. Statically indeterminate beam – For a statically indeterminate beam, equilibrium conditions are not enough to solve reactions. Additional deflections are needed to solve reactions.

• Based on the type of support:

1. Simply supported beam
2. Cantilever beam
3. Overhanging beam
4. Continuous beam
5. Fixed beam

PROCEDURE :

• Geometry Modelling of Beams -
• Case 1. Beam of Rectangular Cross-section,

• A beam of rectangular cross-section is sketched with above dimensions and extruded to a length of 400mm as shown here,

• Case 2. Beam of I Cross-section,

• A beam of I cross-section is sketched with above dimensions and extruded to a length of 400mm as shown here,

• Case 3. Beam of Channel Cross-section,

• A beam of Channel cross-section is sketched with above dimensions and extruded to a length of 400mm as shown here,

• Simulation Setup -
• After sketching models, for finite element analysis, Simulation from Solidworks Add-ins was used. Static Analysis were setup and for all three cases the material defined for the geometry models were 'Alloy Steel'. The properties of 'Alloy Steel' are,

• A fixture were used to fix a face of all the beams to make them act like Cantilever beams and a force of `1500N` were applied on the faces of beams as stated in the challenge statements. Then meshing were done on the beams with the global size of `2.5mm` resulting in a fine meshing. Then it was made to run.
• Case 1. Beam of Rectangular Cross-section,

• Case 2. Beam of I Cross-section,

• Case 3. Beam of Channel Cross-section,

RESULT :

• Case 1. Beam of Rectangular Cross-section,

Stress Plot based on Von-Mises study

Displacement Plot

Eqivalent Strain Plot

Comparison Plots

• Case 2. Beam of I Cross-section,

Stress Plot based on Von-Mises study

Displacement Plot

Eqivalent Strain Plot

Comparison Plots

• Case 3. Beam of Channel Cross-section,

Stress Plot based on Von-Mises study

Displacement Plot

Eqivalent Strain Plot

Comparison Plots

• In addition to these plots, plot for factor of safety were also made and mass propeties of geometries were found out.
• Summary of results in tabular form.

CONCLUSION :

1. For Beam of Rectangular Cross-section, the values of stresses, displacement and equivalent strain are minimum as compared to other beams. The factor of safety for the load applied is also maximum considering other beams. But the weight of the beam is significantly higher than other cases.
2. For Beam of I Cross-section, the values of stresses, displacement, equivalent strain, factor of safety are in between to that of other two cases. The weight of the beam is minimum compared to other beams.
3. For Beam of Channel Cross-section, the values of stresses, displacement, equivalent strain, factor of safety are minimum of all three cases.
4. All these beams can be used for their respective purposes according to the requirement, aesthetics, cost. If the requirement is of resisting most of the bending moment, I section can be used over rectangular beam as it also serves it's purpose almost equally and it requires less material to construct and hence more economical compared to rectangular-section.
5. Moreover, from beam theory, it is well explained that for same weight and length of beams, the flexural rigidity of I-section is more than the flexural rigidity of rectangular section. Hence, I-section is a better choice for bending load.
6. When depths are same, where the full strength of I shaped beams is not needed, C-section beams are used as one can save steel equal to the area of one flange (= 2 half flanges). The I section of the same depth would have been under - stressed and therefore underutilised. The channel section offers a clean and flat surface for the full depth, on one side, that greatly facilitates connections to other member besides being architecturally more pleasing /aesthetic.
7. Out of these three beams, if one has to choose for design purposes, I-section should be given first preference, then Channel-section (C-section) and then beam of rectangular-section.
   

REFERENCES :

https://skyciv.com/technical/benefits-of-different-steel-sections/