KATHMANDU UNIVERSITY SCHOOL OF ENGINEERING

DEPARTMENT OF MECHANICAL ENGINEERING

AnSys Project on

Beam, truss and thermal characteristic

Submitted to

Mr. Krishna Prasad Shrestha

Department of Mechanical Engineering

Kathmandu University

Submitted by

Aatmaram Kayastha(41067)

Amod Panthee(41071)

Rojan Shrestha (41087)

December 9, 2010

Determine the displacement at point C for the steel overhauling beam as shown in the figure. Take 𝐄𝐚 = 𝟐𝟗 × 𝟏𝟎𝟑𝐤𝐬𝐢, 𝐈 = 𝟏𝟐𝟓 𝐢𝐧𝟒.

Solution:

M/EI Diagram: See figure (b)

Elastic curve : The loading causes the beam to deflect as shown in figure (c). We are required to find Δc. By constructing tangents at C and at the supports A and B, it is seen that ∆𝑐= �𝑡𝐶

𝐴�� − ∆𝑡. However, ∆𝑡 can be related to tB/A by proportional triangles; that is,

∆𝑡/24 = |𝑡𝐵𝐴�

|/12 or ∆𝑡= 2|𝑡𝐵𝐴�

|. Hence

∆C= �tCA�� − 2|tB

A�| (1)

Moment Area Theorem: Applying theorem 2 to determine tC/A and tB/A, we have

tC/A = �23 (12)� �

12

(12)�−60EI��+ �

13

(12) + 12� �12

(12)�−60EI�� = −

8640EI

tB/A = �13

(12)� �12

(12)�−60EI�� = −

1440EI

5kip

A B C

12 ft 12 ft

5 kip 10 kip

Figure (a)

𝑀𝐸𝐼

Figure (b) −60

𝐸𝐼

Substituting the results in equation (1) yields

∆C= 8640EI

− 2 �1440EI� ↓ = 5760

EI↓

Realizing that the computations were made in units of kip and ft, we have

∆C== 5760

EI ↓ = 5760 kip ∙ ft3(1728in3/ft3)[29 × 103kip/in2](125 in4) = 2.75in ↓

Source: Page-594, Example 12-12, R.C. Hibbeler, Mechanics of Materials, Macmillan Publishing Company, New York, 1991

AnSys Solution:

Step 1: Change the file name to BEAM

In Utility menu, File>Change Title. A dialog box appears, type the name. and press ok.

tanA

Δt

tanB tB/A tC/A

A B ΔC

tanC

Figure (c)

To view the filename in working pan, click Plot>Replot in Utility menu.

Step 2: Select Prefernces> structural > in AnSys Main Menu and select h-method in same dialog box.

Step 3: Model the beam. Select Preprocessor > Modeling > Create > Keypoints > In active CS.

A dialog box appears, give the co-ordinate of keypoints.

Step 4: Next step is to create the line that represents beam elements. Preprocessor > Modeling > Create > Lines > Lines > Straignt Line as shown in the figure below. And select the keypoints where lines are to be constructed. Press OK in Create Straight Line Window.

Step 5: Next step is to define the element type. Select Preprocessor > Element Type > Add/Edit/Delete. A Element Type Window appears. Select Add. Library of Element Types window appears. Select Beam > elastic 3 and press OK.

Step 6: Next step is to define a real constant. Select Preprocessor > Real Constants > Add/Edit/Delete. A Geenric Real Constant Dialog box appears. Enter the required value in the dialog box.

Step 7: In next step we define the material properties. Select Preprocessor> Material props > Material models. Define material model dialog box appears, select structure>Linear>Elastic > Isotropic. Give the value of Youngs Modulus of Elasticity, and Poissons ratio in the dialog box.

Step 8: Also define the density of the material in material model dialog box.

Step 9: In this step meshing is done. Select Preprocessor > Meshing > Size controls > Manual Size> Lines>All Lines. In no of element entry, enter 1 as we are taking a single element.

Step 10: select preprocessor > meshing > mesh > lines. And select pick all in dialog box.

Step 11: Preprocessor > Analysis type>New Analysis. Select static in dialog box.

Step 12:

In this step load is defined. Solution>define Load> Apply>Structural>Displacement>. Pick the keypoints and enter the value for every point. For a fixed and pin joint different type of degree of freedom is selected.

Step 13: In this step force is defined. Solution> Define Loads>Apply>Structural>Force Moment. Apply F/M on KPs dialog box appears, enter the values considering the direction in dialog box. GUI shows a beam as shown in the image below.

Step 14: In this step gravitational acceleration is applied to the beam. Define Loads>Apply>Inertia>Gravity>Global. Value of g is entered in the dialog box.

Step 15: Next the problem is solved. Solution> Solve>Current LS. Select OK in solve current Load setup window.

Step 16: General postprocessor shows the result of the solved problem. Select General postprocessor>Plot Results>Deformed shapes. Plot Deformed shape dialog box appears, select Def+undef edge, a GUI as shown below appears. Its shows the deflection of point C to be 2.227 inches.

Step 16: In this step nodal solution of problem is seen. Select General postprocessor>Plot Results>Contour Plot> Nodal Solution. Select vector sum in nodal solution when dialog box appears. Its shows the beam stress in different colours.

Step 17: In this step the reaction is obtained at points A,B and C using the Result and Summary tab in General Postproc.

Result: The result deviates from the original calculation in the book. This is because of the material property that we have assigned during simulation. The density of the material is not provided in book. This caused to deviate the result slightly.

Determine the vertical displacement of joint C of the steel truss shown in figure. The cross-sectional area of each member is A = 400mm2, and Ea=200 GPa.

Solution:External Force P: A vertical force P is applied to the truss at joint C, since this is where the vertical displacement is to be determined, Figure (b)

D C

2 m

A B 2 m 2 m 100 kN Figure (a)

141.4kN+1.414P 141.4kN

200kN+P A 450 100kN 100kN 450 B

100kN+P 100kN

Figure (b)

Internal Forces N: The reaction at the truss supports A and D are calculated and the results are shown in figure (b). Using the method of joints, the N forces in each member are determined, Figure (b). For convenience, these results along with the partial derivatives 𝜕𝑁/𝜕𝑃 are listed in tabular form. Note that since P does not actually exist as a real load on truss, we require P = 0.

Member N 𝝏𝑵/𝝏𝑷 N(P=0) L N(𝝏𝑵/𝝏𝑷)×L AB -100 0 -100 4 0 BC 141.4 0 141.4 2.828 0 AC -141.4-1.41∆𝑃 -1.414 -141.4 2.828 565.7 CD 200 + P 1 200 2 400

Σ965.7 kN ∙ m

Castigliano’s second theorem: we have the relation

∆𝑐= ΣN �∂N∂P�

LAE =

965.7 kN ∙ mAE

Substituting the numerical values for A and E, we get

∆𝑐=965.7 kN ∙ m

[400 × 10−6m2] × 200 × 106kN/m2 = 0.01207 m = 12.1 mm

Source: Page-744, Example 14-18, R.C. Hibbeler, Mechanics of Materials, Macmillan Publishing Company, New York, 1991

Ansys solution:

Preprocessing: Defining the Problem

1. Give the Simplified Version a Title (like Truss)

• In the Utility menu bar select File > Change Title:

• Select Utility Menu > Plot > Re-plot

2. Enter Key points

• From the 'ANSYS Main Menu' select: Preprocessor > Modeling > Create > Key

points > In Active CS

3. Form Lines

• In the main menu select: Preprocessor > Modeling > Create > Lines > Lines > In

Active Coordinates

4. Define the Type of Element

• From the Preprocessor Menu, select: Element Type > Add/Edit/Delete

5. Define Geometric Properties

• In the Preprocessor menu, select Real Constants > Add/Edit/Delete

Click Add... and select 'Type 1 LINK1' Click on 'OK'.

6. Element Material Properties

• In the 'Preprocessor' menu select Material Props > Material Models

Double click on Structural > Linear > Elastic > Isotropic

7. Mesh Size

• In the Preprocessor menu select Meshing > Size Controls > Manual Size > Line >

All Lines

8. Mesh

• In the 'Preprocessor' menu select Meshing > Mesh > Lines and click 'Pick All' in

the 'Mesh Lines'

Solution Phase: Assigning Loads and Solving

1. Define Analysis Type

• From the Solution Menu, select Analysis Type > New Analysis.

Ensure that 'Static' is selected;

2. Apply Constraints

• In the Solution menu, select Define Loads > Apply > Structural > Displacement >

On Key points

3. Apply Loads

• Select Define Loads > Apply > Structural > Force/Moment > on Key points.

4. Solving the System

• In the 'Solution' menu select Solve > Current LS.

Post processing: Viewing the Results

1 Reaction Forces

• From the Main Menu select General Postprocessor > List Results > Reaction

Solution.

2 Deformations

• In the General Postprocessor menu, select Plot Results > Deformed Shape.

3 Deflections

• From the 'General Postprocessor' menu select Plot results > Contour Plot > Nodal

Solution.

Thermal Analysis

Pre-processing:

1. Give Jobname 2. Give Title

Preference > Thermal > OK

3. Create Geometry: Preprocessor > Modeling > Create > Areas > Rectangle >By 2 Corners > X=0, Y=0, Width=1, Height=1.

4. Define Element Type: Preprocessor > Element Type > Add/Edit/Delete > click ‘Add’ > Select Thermal Solid, Quad4Node 55

5. Element Material Properties: Preprocessor > Material Props > Material Models > Thermal > Conductivity > Isotropic > KXX=10

6. Mesh Size: Preprocessor > Meshing > Size Controls > Manual size > Areas > All Areas > 0.05

7. Mess: Preprocessor > Meshing > Mesh > Areas > Free > Pick All

Solution Phase:

1. Define Analysis Type: Solution > Analysis Type > New Analysis > Steady-State

2. Apply Conduction Constraints: Solution > Define Loads > Apply > Thermal > Temperature > On Lines

3. Solve The System: Solution > Solve > Current LS

Post processing:

1. Plot Temperature: General PostProcessor > Plot Results > Contour Plot > Nodal Solution > DOF solution, Temperature Temp