Non-side-sway frame with cantilever. Slope Deflection Method

1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantileversSTRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

2. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
CAN YOU SOLVE ALL OF THEM?
HOW MANY DEGREES OF FREEDOM CAN YOU FIND IN EACH FRAME?

3. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
WHAT ABOUT VERTICAL REACTION FORCES? EQUAL OR DIFFERENT IN 1 and 2?
WHAT ABOUT HORIZONTAL REACTION FORCES? EQUAL OR DIFFERENT IN 3 and 4?

4. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
WILL BENDING MOMENTS BE EQUAL IN FRAMES 1 AND 2?
WILL BENDING MOMENTS BE EQUAL IN FRAMES 3 AN 4?

5. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantileversSTRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
CAN YOU GUESS THE SHAPE OF THE BENDING MOMENT DIAGRAMS AND THE
FRAMES DEFORMED SHAPES?

6. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantileversSTRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
TO APPLY THE SLOPE DEFLECTION METHOD WE NEED TO KNOW
THE EFFECT OF LOADS applied along the bars IN THE BAR ENDS
(end moments produced by the loads applied along the bars)
THE EFFECT OF JOINT ROTATIONS IN THE BAR ENDS
(end moments produced by the joints rotations)
THE EFFECT OF JOINT DISPLACEMENTS IN THE BAR ENDS
(end moments produced by the joints displacements)

7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
SLOPE DEFLECTION METHOD STEP BY STEP
ROTATIONS
and
DISPLACEMENTS
END
MOMENTS
SHEAR
FORCES
AXIAL
FORCES

8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
1.- DEGREES OF FREEDOM?

9. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS

10. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS

11. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS

12. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE
EFFECT OF THE ROTATIONS
cv c
v
c
v

13. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE
EFFECT OF THE ROTATIONS

14. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE
EFFECT OF THE ROTATIONS

15. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
4.- DISPLACEMENTS: NOT IN THIS FRAME

16. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
5 and 6.- EQUILIBRIUM EQUATION
𝑴 𝒄 = 𝟎

17. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
7.- END MOMENTS
load
rotation
load load
rotation rotation rotationload

18. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
7.- END MOMENTS

19. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
8.- SHEAR FORCES

20. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
10.- BENDING MOMENT DIAGRAM

21. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
10.- SHEAR FORCE DIAGRAM

22. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
9.- AXIAL FORCES
JOINT C EQUILIBRIUM

23. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
9.- AXIAL FORCES

24. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
11.- DEFORMED SHAPE

25. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
-16,875 mm
+5,75 mm
+5,75 mm
11.- VERTICAL DISPLCAMENT IN THE MIDDLE OF THE SPAN
EFFECT OF THE LOAD
EFFECT OF THE RIGHT MOMENT
EFFECT OF THE LEFT MOMENT

26. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Non-sway frame with cantilevers
1,33 mm
-2,00 mm
11.- VERTICAL DISPLCAMENT AT THE END OF THE CANTILEVER
EFFECT OF THE LOAD
EFFECT OF THE ROTATION