20ME68_Analysis of Bar with Constant Area.pptx

ansys problem on beam with constant strength.

1. Computer Aided Modelling and Analysis Laboratory 20ME68 Exercises Stress analysis of Bars of 1.Constant area Prepared by: Vinayaka G P Course Coordinator, CAMA Lab Department of Mechanical Engineering Vidyavardhaka College of Engineering, Mysuru

2. Analysis of: “Bar of Constant Area”

3. For the simple steel bar of cross-sectional area 500mm 2 ,length 900mm and the Young’s modulus E=2×10 5 N/mm 2 ,Determine the following when it is subjected to the following loads “P”: Tensile load of P= 800N Compressive Load of P=700N Reaction force at the support Nodal stress Deformation. Assume Poison’s ratio of 0.3 P 900 mm Problem Statement

4. Problem Statement Analysis Problem Domain: Structural Element type & its geometry: Bar of Uniform Cross sectional Area. Material and Young’s Modulus: Steel, E =2.1e 5 Cross Sectional Area: 500mm 2 Length of the Element: 900mm Magnitude & Nature of the Load: 800 N tensile and 700N Compressive.

5. Parameters to be Determined

6. Problem Solution by Strength of Material Approach

7. Calculation of Reaction Force Consider Tensile load of P = 800N Considering sum of forces in X -direction Σ𝐹 x = 0 𝑅x+ 𝐹x = 0 𝑅x = -800𝑁 Consider Compressive load of P = 700N Considering sum of forces in X -direction Σ𝐹 x = 0 𝑅x- 𝐹x = 0 𝑅x = 700𝑁 F x R x F x R x

8. Calculation of Stress Consider Tensile load of P = 800N Stress induced in the Bar: F =800N A= 500mm 2 = 1.6 Nmm -2   Consider Compressive load of P = 700N Stress induced in the Bar: F =700N A= 500mm 2 = 1.4 Nmm -2  

9. Calculation of Deformation Consider Tensile load of P = 800N Deformation of the Bar: P =800N L = 900mm A= 500mm 2 E= 2.1e5 Nmm -2 𝛿𝑙= 6.857 × 10 -3 𝑚𝑚   Consider Compressive load of P = 700N Deformation of the Bar: P =-700N L = 900mm A= 500mm 2 E= 2.1e5 Nmm -2 𝛿𝑙= - 6× 10 -3 𝑚𝑚  

10. Problem Solution through ANSYS

11. ANSYS-APDL Procedure Ansys Utility Menu File – Clear and Start New-Read File – ok –Verify –Yes File- Change Title-Enter “Analysis of Bars of Uniform Cross Section”- Ok File – Save as- Save Database to- Type file name as “Analysis of Bar of uniform cross section”-Ok. Main Menu: Material Properties Preferences- Structural-Ok. Preprocessor- Element type –Add/Edit/Delete-Element types-Add-Link-3D Finit stn 180-Close. Preprocessor-Material Props-Material Models- Structural –Linear-elastic-Isotropic-EX: 2.1e5 (Youngs Modulus) –PRXY: 0.3(Poisson’s ratio)- Close. Preprocessor-Sections-Link-Add-Section Data: Link Area -500 (Cross sectional area)-Ok.

12. ANSYS-APDL Procedure Main Menu: Model Creation Preprocessor- Modelling-Create-Nodes-In Active CS: Node Number: 01-Location in Active CS: 0,0,0 (X,Y,Z). Node Number: 02-Location in Active CS: 900,0,0 (X,Y,Z). Preprocessor-Modelling – Elements-Auto Numbered- Thru Nodes- Pick Nodes-Pick Node 1 and 2-Ok. Main Menu: Load Application Preprocessor-Loads-Define Loads-Apply-Structural-Displacement-On Nodes-Pick Node 1-DOFs to be constrained-All DOF-Displacement Value: 0- Ok. Command Prompt-f,2,FX,800.

13. ANSYS-APDL Procedure Solution Solve-Current LS-Ok-Solution is Done-Close. General Post Processor Plot Results- Deformed Shape- Def+Undeformed -Ok- Record deformation Value :DMX =0.00687 List Results-Reaction Solu- All Items-Ok-Record the Reaction force: FX =-800N Nodal Solution- Stress- Von Misses Stress- Record the stress value : 1.6Nmm -2

14. Results: Problem Type Parameters Analytical Approach Experimental Approach Error Bar with Constant Cross Sectional Area 1.Reaction Force 2.Deformation 3.Stress -800 N 6.857 × 10 -3 1.6MPa -800N 0.006857 1.6MPa

15. ANSYS-APDL Procedure For Compressive Load follow the same procedure with P value as given in the problem statement. Compressive Load to be given as: f,2,FX,-700