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STRUCTRAL ANALYSIS OF “CULVERT” CAE ASSIGNMENT

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ANALYSIS REPORT

ON

STRUCTRAL ANALYSIS OF “CULVERT”

AT

NTTF BANGALOR

By

MRIGENDRA SINGH (SPG 06 1514)

POSTGRADUATE IN TOOL ENGINEERING

2015-2017

GUIDE Mr. G.V. Guru Shankar,


2 PGTE NTTF BANGLORE

Acknowledgement

I would first like to thank my thesis advisor Mr. G.V. Guru Shankar of the School of Post graduate at

NTTF. The door to Prof. Mr. G.V. Guru Shankar office was always open whenever I ran into a trouble spot

or had a question about my research or writing. He consistently allowed this paper to be my own work, but

steered me in the right the direction whenever he thought I needed it.

Finally, I must express my very profound gratitude to my parents and to my for providing me with unfailing

support and continuous encouragement throughout my years of study and through the process of

researching and writing this thesis. This accomplishment would not have been possible without them.

Thank you.

Author

Mrigendra Singh Tool Engineering NTTF


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Executive Summery

This report contains a very good step by step analysis of STRUCTRAL ANALYSIS OF “CULVER”.

I tried my best to explain all parameters which should be considered before going for analysis with the help

of Ansys 2014. This report contains all cause and effect explanation. I have explained the element type and

all the golden rules of FEA i.e. geometry creation, material property, loading condition and boundary

condition.

After reading this report you will be able to understand what are the steps you need to take to execute

good mesh data and how you can achieve best results in Ansys 2014.You will learn how to compare results

generated by Ansys software and how you can check it by mathematical



Table of content;

S. NO

Chapter

Page No

1. Introduction 5-6

2. Problem statement 7-8

3. Material Property 9

4. Generate Mesh Data 9-11

5. Load application 11-12

6. Result and Discussion 12-13

7. Appendix 13-14

8. Reference 14

Table of Figures; S,NO Figure Topic Page No

1. 3D View of Culvert 5

2. Stress – Strain Graph for Low carbon steel 6

3. Problem statement 7

4. Element Type 7

5. Plane strain explanation 8

6. Material Property 8

7. Key Point in Geometry creation 9

8. Free and Mapped mesh 9

9. Line mesh 10

10. Area mesh 11

11. Boundary condition 12

12. Appling Load 13

13. Deformation in X direction 13

14. Von Mises stress 14

Note;

All symbols are standard symbols and SI units are uniformly followed.



Introduction;

A culvert is shown in the figure (1); we have to analyze it for maximum deflection and maximum Von

Mises’s stress. It is an elastic problem, so we will take some assumptions of Hooks Law.

Figure 1, 3D View of Culvert

Hooke’s Law: On the application of stress on an elastic body, the strain experienced by the body (amount

of deformation) is directly proportional to the stress applied.

Assumptions for Hooks Law

1) Body is in equilibrium under the action of load.

2) The deformation produced in the body is very small in comparison to the body size.

3) The material of the body is assumed to be linearly elastic.

4) The material is isotropic, homogeneous and continuous.

5) The normal stress will generate normal stain and shear stress will generate only shear strain.



Figure-2, Stress – Strain Graph for Low carbon steel

Stress Strain Curve for low-carbon steel

Hooke's law only valid for portion of curve between origin & yield point (2)

1. Ultimate Strength 2. Yield strength– corresponds to yield point 3. Rupture 4. Strain hardening region 5. Necking region A: Engineering stress (F/A0) Curve

The finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems for partial differential equations. It is also referred to as finite element analysis (FEA). It subdivides a large problem into smaller, simpler parts that are called finite elements. The simple equations that model these finite elements are then assembled into a larger system of equations that models the entire problem. FEM then uses variation methods from the calculus of variations to approximate a solution by minimizing an associated error function. We will perform Stress analysis in Ansys 2014.

For getting correct results we have to define four inputs in Ansys software workbench.

Geometry

Material property

Loads

Boundry condition.



Problem Statement

Figure- 3, Problem statement

Given Data

Load = 0.3 MPa/m2

E= 40 GPa

µ = 0.15

Our very first approach is to define element type in Ansys for this problem. We will first of all define the problem type and selection of elements.

Figure- 4, Element Type

We had selected here a solid as an element type and element behavior as a Plane strain problem.



If one dimension is very large compared to the others, the principal strain in the direction of the longest dimension is constrained and can be assumed as zero, yielding a plane strain condition (Figure 5). In this case, though all principal stresses are non-zero, the principal stress in the direction of the longest dimension can be disregarded for calculations. Thus, allowing a two dimensional analysis of stresses, e.g. a dam analyzed at a cross section loaded by the reservoir.

Figure- 5, Plane strain explanation

Define Material Property (Step-1)

According to assumptions we have considered for this problem we will choose the material property and we will give other input according to the problem statement.

Figure- 6, Material Property



Define Geometry (Step-2)

We have to create geometry for our problem statement then only we can generate nodes and elements, so for creating geometry, we will find coordinates and then we will generate keypoints.

Figure- 7, Key Point in Geometry creation

Now in our next step we will generate area by creating straight lines passing through the keypoints.

Generate Mesh (Step-3)

Before meshing the model, and even before building the model, it is important to think about whether a free mesh or a mapped mesh is appropriate for the analysis. A free mesh has no restrictions in terms of element shapes, and has no specified pattern applied to it. Compared to a free mesh, a mapped mesh is restricted in terms of the element shape it contains and the pattern of the mesh. A mapped area mesh contains either only quadrilateral or only triangular elements, while a mapped volume mesh contains only hexahedron elements. In addition, a mapped mesh typically has a regular pattern, with obvious rows of elements. If we want this type of mesh, we must build the geometry as a series of fairly regular volumes and/or areas that can accept a mapped mesh.

Figure-8, Free and mapped meshes



Figure -9, Line mesh

First of all we have to mesh line elements.

Figure- 10, Area mesh



Now we need to give size control for mesh elements.

Now finally we have to mesh by Free Mesh. It will help up to achieve better mesh quality with better aspect ratio because this surface is not uniform throughout so Mapped mesh will not generate good results.

So we have achieved a good Mesh with very constant aspect ratio now we can proceed for next step.

Load (Step-4)

Figure- 11, Boundary condition



Here we have to select Symmetric boundary condition because we have to maintain thickness of this structure uniform throughout. Only arc can deform no thinning will take place.

Figure- 12, Appling Load

Result , discussion and conclusion

Figure- 13, Deformation in X direction

Maximum displacement in Y direction



Figure- 14, Von Mises stress

Von Mises stress distribution.

So from above results we can conclude that the deformation produced in the body is very small in

comparison to the body size, which is according to our assumption. Stress is concentrated on the arc of the

structure, so it will be better to give reinforcement at the arc or we should increase the thickness of the arc

area.

Appendix;

Stress;

The stress applied to a material is the force per unit area applied to the material. The maximum stress a material can stand before it breaks is called the breaking stress or ultimate tensile stress.

Tensile means the material is under tension. The forces acting on it are trying to stretch the material. Compression is when the forces acting on an object are trying to squash it.

Strain (Deformation);

Strain is defined as "deformation of a solid due to stress" and can be expressed as

ε = dl / lo

= σ / E



Where

dl = change of length (m, in)

lo = initial length (m, in)

ε = strain - unit less

E = Young's modulus (Modulus of Elasticity) (N/m2 (Pa), lb/in2 (psi))

Young's modulus can be used to predict the elongation or compression of an object.

Distortion energy theory;

The concept of Von mises stress arises from the distortion energy failure theory. Distortion energy failure theory is comparison between 2 kinds of energies, 1) Distortion energy in the actual case 2) Distortion energy in a simple tension case at the time of failure. According to this theory, failure occurs when the distortion energy in actual case is more than the distortion energy in a simple tension case at the time of failure.

Expression for Von Mises stress;

The above 2 quantities can be connected using distortion energy failure theory, so the condition of failure will be as follows.

The left hand side of the above equation is denoted as Von Mises stress.

So as a failure criterion, the engineer can check whether Von Mises stress induced in the material exceeds yield strength (for ductile material) of the material. So the failure condition can be simplified as

Reference;

1. Wikipedia

2. Theory of Elasticity – Timoshenko

3. www.ansys.com

https://3.bp.blogspot.com/-GSYvhjsJzps/UN-jHFCAACI/AAAAAAAAAJU/fK-PN1-2W3I/s1600/dist_cond.gif

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