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cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
cperez.eps@ceu.es
molina.eps@ceu.es
LET’S SOLVE THE FOLLOWING SEMI FRAME
(inclined support + horizontal beam)
EQUILIBRIUM EQUATIONS
ARE NOT ENOUGH TO
ANALYZE THE SYSTEM
AS THE DEGREE OF INDETERMINACY IS HIGH
we consider as unknowns the DEGREES OF FREEDOM
so we apply the SLOPE DEFLECTION METHOD
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
HOW DOES THIS FRAME MOVE?
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
EFFECT OF THE LOADS APPLIED ALONG THE BARS
M=0
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
WE MAKE JOINT B ROTATE AND WE MEASURE THE EFFECT OF THIS ROTATION
M=0
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
WE MAKE JOINT A MOVE AND WE MEASURE THE EFFECT OF THE MOVEMENT
M=0
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
REMEMBER: END MOMENTS DUE TO THE DISPLACEMENT APPEAR ONLY IN
BARS THAT ROTATE AS A CONSEQUENCE OF THE DISPLACEMENT
M=0
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
HOW MANY EQUILIBRIUM EQUATIONS?
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
FIRST EQUATION: S MB = 0
SECOND EQUATION?
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
SECOND EQUATION? IT IS INTERESTING FINDING A EQUATION IN WHICH
NO AXIAL FORCES ARE INVOLVED
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
SECOND EQUATION? IT IS INTERESTING FINDING A EQUATION IN WHICH
NO AXIAL FORCES ARE INVOLVED
AT O THE AXIAL FORCE ALONG BC AND THE VERTICAL REACTION FORCE AT A INTERSECT
S MO = 0
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
END MOMENTS
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
END MOMENTS AND SHEAR FORCES
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
SHEAR FORCE DIAGRAM
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
AXIAL FORCES (ANALYSING JOINT B FIRST
AND WHAT HAPPENS ALONG AB THEN)
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
AXIAL FORCE DIAGRAM
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
BENDING MOMENTS DIAGRAM AND DEFORMED SHAPE
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
THINK ABOUT WHAT HAPPENS IN THESE FRAMES
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
THINK ABOUT WHAT HAPPENS IN THESE FRAMES
cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
SLOPE DEFLECTION METHOD
Inclined support + beam with roller
THINK ABOUT WHAT HAPPENS IN THESE FRAMES

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