Ae1 20 21_sb_s_inclined supports frame_slope deflection_

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The document discusses applying the slope deflection method to analyze an inclined supports frame structure. It explains that the slope deflection method requires determining the effect of loads, joint rotations, and joint displacements on end moments. Three degrees of freedom must be considered: rotations at joints D and E, and the horizontal displacement at joint D. The method involves determining relationships between displacements, then setting up and solving equilibrium equations.

Engineering

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
DEGREE OF INDETERMINACY?
DEGREES OF FREEDOM?

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
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)

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
SLOPE DEFLECTION METHOD STEP BY STEP
ROTATIONS
and
DISPLACEMENTS
END
MOMENTS
SHEAR
FORCES
AXIAL
FORCES

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
DEGREES OF FREEDOM?

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
THREE DEGREES OF FREEDOM to consider:
rotations at D and E+ horizontal displacement at D

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
EFFECT OF THE LOAD: only loads applied along the bars

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
EFFECT OF THE ROTATION: we make joints D and E rotate

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
EFFECT OF THE DISPLACEMENT: we make joint D move horizontally

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
RELATIONSHIP AMONG THE DISPLACEMENTS

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
EQUILIBRIUM EQUATIONS?

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
DIFFERENCES?

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
NO END MOMENT ZERO

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined supports frame
ONE END MOMENT ZERO

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