Ae1 1920 class 4_10_03

cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
19/20 CLASS 4
cperez.eps@ceu.es
molina.eps@ceu.es
CASA ENTRE TAPIALES. JESÚS DONAIRE 2017
STATICALLY inDETERMINATE BEAMS AND FRAMES
SLOPE DEFLECTION METHOD

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
STATICALLY INDETERMINATE STRUCTURES. SLOPE DEFLECTION METHOD
CONTINUOUS BEAM
NON-SWAY FRAME

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
SLOPE DEFLECTION METHOD versus COMPATIBILITY METHOD
WHAT WOULD YOU DO IF YOU HAD TO SOLVE THIS CONTINUOUS BEAM?

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
WHAT DO YOU HAVE TO DO TO APPLY COMPATIBILITY?...
3
COMPATIBILITY
EQUATIONS
3 UNKNOWNS
12 ROTATION
EXPRESSIONS!!!!

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
WHEN THE DEGREE OF INDETERMINACY IS HIGH,
THE NUMBER OF DEGREES OF FREEDOM IS LOW
SO IT IS LESS TIRING TO APPLY THE SLOPE DEFLECTION METHOD
INSTEAD OF THE COMPATIBILITY METHOD

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
EQUATIONS UNKNOWNS COEFFICIENTS
Compatibility Method
(force method or flexibility
method)
COMPATIBILITY between
movements (rotations or
displacements)
Redundant reaction forces
or Moments or internal
forces or moments
Flexibility coefficients(L/EI)
Slope Deflection Method
(equilibrium method or
displacement method)
EQUILIBRIUM of end
moments or joint forces
MOVEMENTS: rotations or
displacements
Bending stiffness (EI/L)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
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
Year 3 Term 1
19/20 CLASS 4
LOAD ALONG THE BARS EFFECT

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
LOADS EFFECT

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
ROTATION EFFECT

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
DISPLACEMENT EFFECT

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
LET’S SOLVE THIS BEAM APPLYING THE SLOPE DEFLECTION METHOD
THIS METHOD IS ATTRACTIVE IN THIS CASE BECAUSE
THE DEGREE OF INDETERMINACY IS HIGH
THERE IS ONLY ONE DEGREE OF FREEDOM:
the rotation at B

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
SLOPE DEFLECTION METHOD STEP BY STEP
1.- HOW MANY DEGREES OF FREEDOM ARE THERE?
(degrees of freedom = unknowns)
2.- WE FIX THE JOINTS AND ANALYSE THE EFFECT OF THE LOAD
DISTRIBUTED ALONG THE BAR IN THE BAR ENDS (end moments
produced by the loads applied along the bars)
3.- WE MAKE THE JOINTS (which rotation is unknown) ROTATE
AND ANALYSE THE EFFECT OF THIS ROTATION IN THE BAR
ENDS (moments produced by the joints rotation)
4.- WE MAKE THE JOINTS (which displacement is unknown)
MOVE IN THE DIRECTION OF THE UNKNOWN DISPLACEMENT
AND ANALYSE THE EFFECT OF THIS MOVEMENT IN THE BAR ENDS
(moments produced by the joints displacements)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
5.- WE WRITE DOWN THE EQUILIBRIUM EQUATIONS (sum
of the moments at the joints should equal zero)
6.- WE SOLVE FOR OUR UNKNOWNS: ROTATIONS AND
DISPLACEMENTS.
7.- ONCE WE KNOW THE VALUES OF THE ROTATIONS AND
DISPLACEMENTS WE CAN CALCULATE THE BARS END MOMENTS
WATCH OUT!
END MOMENTS ARE NOT EQUAL TO BENDING
MOMENTS!

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
8.- Once we know the values of the end moments WE CAN
CALCULATE SHEAR FORCES.
9.- Once we know the values of the shear forces WE CAN ANALYSE
JOINTS EQUILIBRIUM AND SOLVE FOR AXIAL FORCES.
10.- FINALLY WE CAN DRAW ALL THE DIAGRAMS: BENDING
MOMENTS DIAGRAM (also after 7), SHEAR FORCE DIAGRAM (also
after 8), AXIAL FORCE DIAGRAM.
11.- THE DEFORMED SHAPE SHOULD CONSIDER BOTH THE
ROTATIONS AND DISPLACEMENTS OBTAINED IN 6 AND THE
BENDING MOMENTS DIAGRAM. WE CAN ALSO CALCULATE
EASILY DISPLACEMENTS IN THE MIDDLE OF BEAMS SPANS.

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
ROTATIONS
and
DISPLACEMENTS
END
MOMENTS
SHEAR
FORCES
AXIAL
FORCES

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
DEGREES OF FREEDOM?
or which movements (displacements or rotations) are possible?
NUMBER OF UNKNOWNS?
NUMBER OF EQUILIBRIUM EQUATIONS?

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(1)
(2)
(3)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(5) S M = 0
B
EQUILIBRIUM EQUATION

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
-41,66 + 18,75 + 8000 gB + 13333,33 gB = 0gB = 1,074 mrad
EQUILIBRIUM EQUATION(5) S M = 0
B

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(6)
END MOMENTS
load
rotation
WATCH OUT!
END MOMENTS ARE NOT EQUAL TO BENDING
MOMENTS!

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(7)
END MOMENTS

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(8) SHEAR FORCES

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(10)
(11)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
DEGREES OF FREEDOM?
or which movements (displacements or rotations) are possible?
(1)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(2)
EFFECT OF THE LOAD

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(3)
EFFECT OF THE JOINTS ROTATION

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(5)
(6)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(7) END MOMENTS

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
HOW TO CALCULATE SHEAR FORCES IN INCLINED BARS?
(9)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
HOW TO CALCULATE SHEAR FORCES IN INCLINED BARS?

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(8)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(10)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(9)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
(11)

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
HOW WOULD THE PROCCESS AND THE RESULTS CHANGE IF THE
SUPPORTS ARE PINNED INSTEAD OF FIXED?

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
2016/2017 CLASS 4c
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

cperez.eps@ceu.es
molina.eps@ceu.es
Year 3 Term 1
19/20 CLASS 4
2017/2018 CLASS 4

Ae1 1920 class 4_10_03

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Ae1 1920 class 4_10_03