Link Element Example is solved using basic concepts of Applied Mechanics, and the results are then to be verified from ANSYS

1. Applied Mechanics Exercise
Analysis of Frames
VAFTSY CAE

2. E=180GPa P.R 0.23 C/S 0.01sqm
1000N
10m 10m
Fix
10m
10m Uy=0

3. Free Body Diagram
1000N R5y
10m 3 10m R5x
1 5
10m
4
2 10m
R4y

4. É Fy=0
Applying Equilibrium
-
1000N R5y 1000+R4y+R5y=0
10m 3 10m R4y+R5y=1000
R5x
1 5
É Fx=0
10m R5x =0
Sum M@5=0
-1000 x 20 +R4y x 5 = 0
4
2 10m 5 R4y = 20000
R4y+R5y=1000
4000+R5y=1000 R4y=4000
R4y
R5y = -3000
+ve

5. 1000N R5y= 3000
10m 3 10m R5x = 0
1 5
10m
4
2 10m
R4y = 4000

6. Determination of Corner Angle
1000N
10m
5m
F13 3
1
1 A
A
10m
F12
2 A = tan -1 (10/5)
2
A= 63.43 deg

7. Resolution of Forces at Node
1000N 1000N
F13 3
F13
1 1
A
A
F12 F12
2 F12 Cos A
1
A = tan -1 (10/5)
A
F12 Sin A
A= 63.43 deg
F12

8. 1000N 1000N
F13 3
F12 Cos A F13
1 1
A
F12 F12 Sin A
2 F12 Cos A
1
A = tan -1 (10/5)
A
F12 Sin A
A= 63.43 deg
F12

9. Summation of Nodal Forces
1000N 1000N
F13 3
F12 Cos A F13
1 1
A
É Fy=0
F12 F12 Sin A
-1000 - F12 Sin A = 0
F12 Sin A = -1000
É Fx=0 F12 = (-1000/Sin
2 63.43)
F12 Cos A + F13 = 0
A = tanF13(10/5) Cos A
-1 = - F12 F12= -1118.19
F13= - ( -1118.19 Cos
63.43)
A= 63.43 deg
F13= 500.15

10. ANSYS Model

11. Results

12. ANSYS Results reaction solution
THE FOLLOWING X,Y,Z SOLUTIONS ARE IN THE GLOBAL
COORDINATE SYSTEM
NODE FX FY
4 4000.0
5 0.90949E-12 -3000.0
TOTAL VALUES
VALUE 0.90949E-12 1000.0

13. Element Loads
EL= 1 NODES= 1 2
TEMP = 0.00 0.00 FLUENCES = 0.000E+00 0.000E+00
MFORX= -1118.0
SAXL=-0.11180E+06
EL= 2 NODES= 1 3
TEMP = 0.00 0.00 FLUENCES = 0.000E+00 0.000E+00
MFORX= 500.00
SAXL= 50000.

14. Summary
No Theoretical ANSYS
F12 -1118.9 -1118.8
F13 500.15 500
R4y 4000 4000
R5y -3000 -300
Results show a close match