Strength of Materials

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Strength of Materials


C
OMSOL

Assignment












David Friesorger

14.12.2011

PTE 3



Table of Contents

1.

Introduction Page: 3


2.

Objectives Page: 3



3.

Theory: Page: 4


4.

Method: Page: 5



5.

Results: Page: 6


6.

Discussion:

Page: 6



7.

Conclusion: Page: 6


8.

References: Page: 7


9.

Figures


a.

Edge Load (von Misers) Page: 8

b.

Edge Load (Displacement Page: 8

c.

Point Load (von Misers) Page: 9

d.

Point Load (Displacement Page: 9


Appendix A: Page: 10




Introduction
-

The

purpose of this assignment is to measure by hand calculations and through the use of
C
OMSOL

4.2 important parameters of a t
-
shaped steel beam under a certain axial load.


Objectives
-

1)

Calculate the following by hand. Show all working and units. (Refer to
Figure 1)


a)

The distance y to the center

of mass of the section from the bottom of the section.

b)

The moment of inertia (area) of the section.

c)

The moment created about the centroid.

d)

The maximum normal stress (F/A) created by the axial force.

e)

The stress at
the top and bottom of the section due to bending.

f)

The maximum total stress in the section due to bending and axial loading.

g)

The maximum displacement in the x
-
axis of the section. (Vihtonen

p.1
)



2) Using COMSOL 4.2, 3D structural mechanics, complete an a
nalysis of the section.

-
Produce a surface plot showing the stress and displacement of the section

-
State the values of maximum stress (1
st

principle stress) using both a point load and edge
load.

-
Also determine the x
-
displacement obtained with COMSOL
4.2.

-
Compare and explain the results to those obtained in part 1). (Vihtonen

p.1
)









Theory
-

This analysis is based on the theory that a steel beam under a certain axial load will result in
stresses caused by load, stresses caused by internal
moments, and a resulting displacement of
the beam.

Young

s Modulus for Steel AISI 4340 is

205GPa



The following formulae were used in the hand calculations:




= P/A




=Stress



=⁍ /I



P=Force


=PL/(AE)



A=Area

I = bh
3
/12 (Rectangle),


M=Moment

I
x
=
I
c
+Ad
2



I=Moment of Inertia

M=Fd



E=Young’s Modulus

Y

䄠㴠





L=Length





=deformation





h=height




b=breadth










Method
-

For hand calculations refer to Appendix A.

The method used in C
OMSOL 4.2

is as follows:

1.

Select 3D in select space
dimension

2.

Select Structural Mechanics in ”Add Physics” tab

3.

Select Stationary in ”Select Study Type” tab

4.

Right click geometry in the model builder tab and select Work Plane

5.

Select subheading Geometry under work plane heading.

6.

Proceed to draw T
-
shape with dr
aw line command

as per figure A

7.

Extrude beam to .1 m

8.

Set the material to be Steel AISI 4340

9.

Apply a fixed constraint to one side

10.

Apply an Edge Load

of 10000N

11.

Under mesh tab select build all

12.

Select Study and Compute

13.

Create 3d plot group with displaying
total displacement

14.

Save

15.

Repeat steps 1
-
14
, while replacing step 10 by drawing the point and Apply a point
load of 10000N

16.

Record results














Results
-


COMSOL Results:

Edge Load:

von Mises Stress=1.0159*10
8

N/m
2




Displacement=1.1158*10
-
5

m



Point Load:

von Mises Stress= 1.0898*10
9

N/m
2




Displacement= 4.4163*10
-
5

m


Hand Calculations:

Maximum Stress= 8.54*10
6

N/m
2



Maximum Displacement=
4.16*10
-
6

m



Discussion
-

The results show that the maximum stress and maximum displacement found through

calculations and through the use of COMSOL 4.2 are vastly different. From my understanding
this is due to the fact that through hand calculations we take into account the whole cross
sectional area when calculating the Normal Stress. While COMSOL most lik
ely calculates the
Normal Stress

and maximum displacement

from the edge of the beam alone, which greatly
reduces the area to be considered.


Conclusion
-

After comparing the results of the hand calculations and the results from COMSOL it is clear
that the m
ethods taken to arrive at the final answers were different. It would be interesting to
compare the results of the two methods in an attempt to find the mechanics that are used in
COMSOL.






References
-


Vihtonen, Mathew. Strength of Materials 2011
-
2012.
ARCADA
-

Plastics

Technology/Plastteknik. 28
-
9
-
2011.