Analysis of an I-Beam

Engineering Simulation

Analysis of an I-Beam MEng

Emma Rose Latham (s5127929) 12-13-2019

Engineering Simulation: Analysis of an I-Beam by Emma Rose Latham s5127929

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Abstract

Leading from the Engineering Simulation module, this report contains a comparison between two near-

identical scenarios involving an I-Beam which is fixed at one end and has a force applied at the opposite.

Using the Computer Aided Design software SolidWorks, and its Finite Element Analysis capabilities, scenarios

were simulated to calculate certain parameters about the experiment. To validate these, analytical

techniques are also employed, and the results are discussed in the following report

Table of Contents

Contents Abstract ............................................................................................................................................................... 1

Table of Contents ................................................................................................................................................ 1

Introduction ......................................................................................................................................................... 2

Methodology ....................................................................................................................................................... 2

Results and Discussion......................................................................................................................................... 4

von Mises Stress (downwards) ........................................................................................................................ 4

Displacement (downwards) ............................................................................................................................. 5

Equivalent Strain (downwards) ....................................................................................................................... 6

Von Mises Stress (upwards) ............................................................................................................................ 7

Displacement (upwards).................................................................................................................................. 8

Equivalent Strain (upwards) ............................................................................................................................ 8

Plastic Moment (applicable to both) ............................................................................................................... 9

Stress Concentration (both upwards and downwards) ................................................................................. 12

Conclusions .................................................................................................................................................... 13

References ......................................................................................................................................................... 13


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Introduction

An I-Beam consists of two horizontal planes (flanges) connected by the one vertical (the web) which

together create an I (H) cross-section- giving the beam its name. The I-Beam is the choice shape for

structural builds due to their high functionality; they are excellent for unidirectional bending

parallel to the web. This is because the horizontal flanges resist the bending moment, while the

web resists the shear stress. Available in a variety of configurations, the versatility and

dependability of I-Beams make them a coveted recourse for engineers. (Brakefield, n.d.)

Finite Element Analysis is a

numerical method for solving

problems of engineering physics;

it become useful for solving

complicated problems involving

geometrics, loadings and material

properties and can be used in

combination with analytical

solutions. (Saeed, 2019)

The task which will be analysed in this assignment involves an I-Beam of length 121cm and

dimensions shown in figure 1 with one fixed end whilst the other is loaded both in the downwards

and upwards direction with 450N. These are known as the boundary conditions in the simulation

and allow us to use this data to calculate the unknowns about the system. The FEM software used

is SolidWorks and within the program the material was set to carbon steel assuming tangential

modulus of 3.1e7 psi. This is a common material choice for an I-Beam in structural engineering (it

can often be referred to as structural steel) and means that the simulation is very applicable to

industry.

Methodology

To complete any finite element analysis (FEM) with computer- aided design (CAD) a finite element

mesh needs to be created of the part. It divides the CAD model into domains called elements over

which the equations are solved. These equations approximate the result for the simulations and

Figure 1 Hand- drawn diagram of I-Beam set-up


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since they are governed via a set of polynomial equations, as these elements are made smaller, the

CAD solution should approach the true solution. (Comsol inc., 2017)

Before running the

simulation, I made some

alterations to the

automatically created mesh

of the beam. I made sure to

increase the concentration of

the mesh in the highest area

of the stress in order to make

the end figure more accurate.

The mesh used for the simulation

models is unstructured and is a

more general mesh (which can be

used to approximate more complex

shapes.) The four areas which I

chose to edit were the inner fillets

of the I- Beam where there is a

stress concentration due to the convergence of stress flow. This meant that overall the mesh was

described overall as ‘fine’ by SolidWorks.

If I had a better understanding of SolidWorks and greater time allowance for the report, I could

have manually adjusted the mesh to maximise its efficiency. By leaving elements which are known

to not be of interest to the simulation to be larger means that computational time is not wasted but

the accuracy of the results would increase.

Figure 2: Selection of inner fillets in Solidworks to edit mesh

Figure 3 Close up image showing mesh within flanges of beam.


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An option could be to increase the concentration of the mesh to the finest option within

SolidWorks to maximise the accuracy, but this is inefficient for the computer programme and also

in a real industry example it cretes unnecessary calculations.

Results and Discussion Once the changes to the mesh had been made, CAD quickly and accurately approximates the

simulation and will demonstrate this visually. Often using a colour scale where the largest values

are red to the minimum values as blues, they offer a more user- friendly demonstration of the data

that is gathered.

von Mises Stress (downwards)

The first FEM simulation result is the von Mises Stress which is a metric measurement to determine

whether the structure has started to yield at the given boundary conditions. The stresses are

written into a scalar quantity which can then be compared with experimentally observed yield

points (the yield stress). (Harish, 2019)

Figure 4 Overview of Beam mesh - shows difference in concentration of elements.

Figure 5 SolidWorks Screen Capture of Stress simulation


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It can be seen from the key to the right of the

simulated image that the minimum value

occurred in node location 40696 with a value

of 2.171x10^3 N/m^2. The maximum

occurred at node location 23943 1.247x10^7

N/m^2. The greatest von Mises stress will

occur at the point which greatest force unit

area which is the loaded area, in the join

between the top flange and the web. This is

because the force has been set to be spread between the two vertices of the edge, creating a bend

in the flange.

Otherwise, if the load was concentrated to the centre of the vertices, the greatest area of von

Mises Stress would be the area which is currently second to it. The section of the beam which has

second greatest von Mises Stress is where there is the greatest elastic energy of distortion; which

occurs at the flanges closest to the fixed end of the beam. Here, the full force on the beam is felt

through a relatively small surface area of the cross- section, creating high stress concentration.

The minimum von Mises Stress occurs on the bottom flange of the beam at the loaded end because

very little force is exerted on this area.

Displacement (downwards)

The second study run on the simulation was to visualize the displacement of the beam. Although

initially it presents as one of the most dramatic studies, the maximum displacement is at the end

(node 3095) which is loaded is 1.655x10^-1 mm. This is due to the high strength of the plain carbon

Figure 6 Close image of SolidWorks simulation of Stress

Figure 7 SolidWorks screen capture of displacement


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steel material, which has undergone very minimal deflection under the 450N weight. The minimum

displacement of the beam occurs nearest to fixed end, which is assumed as zero since the

displacement is so small. This simulation is straight forward in explanation.

Equivalent Strain (downwards)

The third data set demonstrated in Solidworks is the Equivalent Strain of the beam. Strain is defined

as the extension of the object over the unloaded length of the object; equivalent strain involves all

the points of an element in an FEM model placed in a matrix to create a three-dimensional

representation. Strain is a useful representation of the data since it shows the displacement within

the elements of the beam (rather than the beam from an outside prospective.) (PP Benham, 1996)

The maximum strain occurred at element 160 with a value of 3.487x10^-5 which is within the top

flange at the loaded end of the beam. Here, the flex in the flange adds to the strain within the

curved of the underside. The elements will be compressed in the vertical direction whilst elongated

in the horizontal- leaving the shape under a large

amount of strain.

The minimum strain occurs at element 8561 with a

value of 1.497 x10^-8 which is on the bottom edge

of the bottom flange at the end which is loaded. This

is because there is very little deformation in the

elements in this area due to other elements being

deformed first since they undergo a greater amount

of stress.

Figure 8 SolidWorks screen capture of Strain simulation

Figure 9 Close image of SolidWorks Strain simulation


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Von Mises Stress (upwards)

Figure 10 von Mises SolidWorks screen capture

The maximum value for von

Mises Stress 1.215x 10^7

N/m^2 occurred at the

bottom flange at the

location where the force is

applied. The minimum

value is 2.201x10^3 along

the top flange of the beam.

The stress is the value

which varies the least in the

simulations because it takes

into account the area it

occurs over.

Figure 11 Close image of SolidWorks simulated Stress


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Displacement (upwards)

Figure 12 SolidWorks Simulation of Displacement

The displacement of the upwards force was identical to the downwards force. This is expected, but

also since there is only a small displacement across the beam and comparatively large

measurement increments the measurements are less precise.

Equivalent Strain (upwards)

Figure 13 SolidWorks simulation of equivalent strain

The strain maximum value is 3.115x 10^-5 and the minimum value is 9.993x10^-9; which again, are

very minute differences in strain, overall and comparatively.


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Figure 14 Close image of highest strain area on SolidWorks

Plastic Moment (applicable to both)

The Plastic Moment, also known as the Plastic Hinge, it is the hypothetical bending moment for

which the stresses in all fibres of a section of a ductile member in bending reach the lower yield

point. Under this condition the section cannot accommodate any additional load. (Warren C.

Young, 2002)


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Using an example and the knowledge that plastic stress is equal to plastic moment, I calculated

that:

This is a reasonable figure when compared with other examples of other similar beams given to us

in our Engineering Simulation module.

Finding the Plastic Moment in SolidWorks turned out to be complex, as there was confusion as to

whether the maximum stress of the maximum strain in the Y- Normal gave the value for the beam.

Figure 15 Handwritten notes of Plastic Moment calculations


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Once consulting with the sources available it was evident that the Strain gave the plastic moment

figure.

Figure 16 Plastic Strain in the Y-Normal on Solidworks

Figure 17 Plastic Strain in Y Normal on Upwards direction

The Plastic moments for the downwards and upwards directions given via a simulation method are

6.42x10^-6 N/m^2 and 6.408x10^-6 N/m^2. As expected, they are almost identical which is what

we had assumed from the analytical method. Gravity is not considered in SolidWorks so there is no

change in the force acting upon the beams between the two scenarios.

The large discrepancy between the analytical and simulated method can be explained through the

inaccuracies in the mesh calculations which due to SolidWorks algorithm and automatically created

mesh will create differences when the direction of the force changes.


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Stress Concentration (both upwards and downwards) Stress concentration is defined as localized stress considerably higher than average due to abrupt

changes in geometry or localised loading. (Safih, 2012) The stress concentration factor is a

demonstrative ratio which compares the ratio of highest equivalent stress to a reference stress.

Figure 18 Handwritten Notes Calculating Stress Concentration Factor

The minimum value is known as the nominal value in this situation.

To understand stress and concentration factor within FEA it must be understood that when there is

an abrupt corner in the model, as the mesh is refined to smaller and smaller elements, stress will

continue to rise. As the size of the elements approaches zero, the stress will tend to infinity. This is

my it is crucial that the model has the fillets in its edges.

Once the radius in the corner has been created, the stress will approach the calculated value from

the Roark and Young’s equation. Here, as the mesh improvement (element size reduction) the

stress value becomes more accurate. This is due to the method of calculation that SolidWorks

employs.


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Conclusions

Simulated Results:

Name Downwards Direction Upwards Direction

Von Mises Stress MIN (N/m^2) 2.171e+03 2.201e+03

Von Mises Stress MAX (N/m^2) 1.247e+07 1.215e+07

Resultant Displacement MIN (mm)

0.000e +00 0.000e+00

Resultant Displacement MAX (mm)

1.655e-01 1.655e-01

Equivalent Strain MIN 1.497e-08 9.999e-09

Equivalent Strain MAX 3.487e-05 3.115e-05

Plastic Moment 1.516e+05 1.516e+05

Stress Concentration Factor 5.744e+03 5.520e+03 Figure 19 Table of Simulated Data

As can be seen from the table above, there is very little difference between the values for the upwards and

downwards simulations. This can be expected since there is no variance in the boundary conditions between

the two different scenarios. Any small difference can be put down to calculation inaccuracies created in

SolidWorks and its use of significant figures and the mesh set- up. The variance between the values can be

explained due to the mesh because it is likely that the mesh in both studies were not completely accurate.

References

Brakefield, K., n.d. Why are I-Beams Used in Structural Steel Construction?. [Online]

Available at: https://blog.swantonweld.com/i-beams-in-structural-steel-construction

[Accessed 07 12 19].

Comsol inc., 2017. Finite Mesh Refinement. [Online]

Available at: https://uk.comsol.com/multiphysics/mesh-refinement


Harish, A., 2019. What is the Meaning of the Von Mises Stess and the Yield Criterion?. [Online]

Available at: https://www.simscale.com/blog/2017/04/von-mises-stress/

[Accessed 09 12 2019].

PP Benham, R. C. C. A., 1996. Mechanics of Engineering Materials. Second ed. Harlow: Pearson Education

Limited.

Saeed, D. A., 2019. Engineering Simulation Lecture Series. [Online]

Available at: https://brightspace.bournemouth.ac.uk/d2l/le/content/68602/viewContent/434136/View


Safih, 2012. Stress Concentration Fundamentals. [Online]

Available at:

https://www.engineersedge.com/material_science/stress_concentration_fundamentals_9902.htm

[Accessed 10 12 2019].

Warren C. Young, R. G. B., 2002. Roark's Formulas for Stress and Strain. Seventh ed. New York: McGraw- Hill.

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Analysis of an I-Beam

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