SlideShare a Scribd company logo
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
Degree in Architecture
Year 3 Term 1
EPS USPCEU
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STATICALLY INDETERMINATE STRUCTURES. SLOPE DEFLECTION METHOD
TEST 3_year 16_17
SLOPE DEFLECTION METHOD. NON-SWAY FRAME
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
CAN YOU SOLVE ALL OF THEM?
HOW MANY DEGREES OF FREEDOM CAN YOU FIND IN EACH FRAME?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
WHAT ABOUT VERTICAL REACTION FORCES?
AND WHAT ABOUT HORIZONTAL REACTION FORCES?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
WILL BENDING MOMENTS BE EQUAL IN FRAMES 1 AND 2?
WILL BENDING MOMENTS BE EQUAL IN FRAMES 3 AN 4?
STRUCTURAL 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?
STRUCTURAL 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)
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
LOAD ALONG THE BARS EFFECT
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
ROTATION EFFECT
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
DISPLACEMENT EFFECT
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
ROTATION EFFECT
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
SIMPLIFIED FORMULAS
USED WHEN ONE OF THE BAR END MOMENTS IS ZERO
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
SIMPLIFIED FORMULAS
USED WHEN ONE OF THE BAR END MOMENTS IS ZERO
BE CAREFUL! WE SHOULD BE CONSISTANT!!!
IF WE CONSIDER M=0 WHEN COMPUTING ROTATION EFFECTS WE
SHOULD ALSO CONSIDER M=0 WHEN COMPUTING LOADS EFFECT AND
DISPLACEMENTS EFFECTS
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
NO END MOMENT ZERO
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
ONE END MOMENT ZERO
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
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)
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
SLOPE DEFLECTION METHOD STEP BY STEP
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!
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
SLOPE DEFLECTION METHOD STEP BY STEP
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.
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
SLOPE DEFLECTION METHOD STEP BY STEP
ROTATIONS
and
DISPLACEMENTS
END
MOMENTS
SHEAR
FORCES
AXIAL
FORCES
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
1.- DEGREES OF FREEDOM?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE
EFFECT OF THE ROTATIONS
cv c
v
c
v
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE
EFFECT OF THE ROTATIONS
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE
EFFECT OF THE ROTATIONS
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
4.- DISPLACEMENTS: NOT IN THIS FRAME
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
5 and 6.- EQUILIBRIUM EQUATION
𝑴 𝒄 = 𝟎
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
7.- END MOMENTS
load
rotation
load load
rotation rotation rotationload
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
7.- END MOMENTS
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
8.- SHEAR FORCES
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
10.- BENDING MOMENT DIAGRAM
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
10.- SHEAR FORCE DIAGRAM
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
9.- AXIAL FORCES
JOINT C EQUILIBRIUM
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
9.- AXIAL FORCES
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
11.- DEFORMED SHAPE
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
-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
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
1,33 mm
-2,00 mm
11.- VERTICAL DISPLCAMENT AT THE END OF THE CANTILEVER
EFFECT OF THE LOAD
EFFECT OF THE ROTATION
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4b
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 4
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

More Related Content

What's hot

Ae1 1920 class 4_10_03
Ae1 1920 class 4_10_03Ae1 1920 class 4_10_03
Ae1 1920 class 4_10_03
Pérez Gutiérrez María Concepción
 
Ae1 1920 class 5_10_8
Ae1 1920 class 5_10_8Ae1 1920 class 5_10_8
Ae1 21 22_class 3_statically indeterminate_class
Ae1 21 22_class 3_statically indeterminate_classAe1 21 22_class 3_statically indeterminate_class
Ae1 21 22_class 3_statically indeterminate_class
Pérez Gutiérrez María Concepción
 
Ae1 1920 class 3_09_13
Ae1 1920 class 3_09_13Ae1 1920 class 3_09_13
Ae1 1920 class 3_09_13
Pérez Gutiérrez María Concepción
 
Ae1 21 22_class 7_slope deflection_side sway
Ae1 21 22_class 7_slope deflection_side swayAe1 21 22_class 7_slope deflection_side sway
Ae1 21 22_class 7_slope deflection_side sway
Pérez Gutiérrez María Concepción
 
Ae1 19 20_2_test 2
Ae1 19 20_2_test 2Ae1 19 20_2_test 2
Ae1 19 20_class 2_09_10
Ae1 19 20_class 2_09_10Ae1 19 20_class 2_09_10
Ae1 19 20_class 2_09_10
Pérez Gutiérrez María Concepción
 
Ae1 21 22_class 8_matrix
Ae1 21 22_class 8_matrixAe1 21 22_class 8_matrix
Ae1 21 22_class 8_matrix
Pérez Gutiérrez María Concepción
 
Ae1 19 20_1_beam with cantilvers
Ae1 19 20_1_beam with cantilversAe1 19 20_1_beam with cantilvers
Ae1 19 20_1_beam with cantilvers
Pérez Gutiérrez María Concepción
 
Ae1 19 20_2_test 1
Ae1 19 20_2_test 1Ae1 19 20_2_test 1
Ae1 21 22_class 2_statically determinate systems_examples
Ae1 21 22_class 2_statically determinate systems_examplesAe1 21 22_class 2_statically determinate systems_examples
Ae1 21 22_class 2_statically determinate systems_examples
Pérez Gutiérrez María Concepción
 
Ae1 20 21_class 7_slope deflection_side sway
Ae1 20 21_class 7_slope deflection_side swayAe1 20 21_class 7_slope deflection_side sway
Ae1 20 21_class 7_slope deflection_side sway
Pérez Gutiérrez María Concepción
 
Ae1 21 22_sb_s_semi frames_slope deflection_settlements_side sway
Ae1 21 22_sb_s_semi frames_slope deflection_settlements_side swayAe1 21 22_sb_s_semi frames_slope deflection_settlements_side sway
Ae1 21 22_sb_s_semi frames_slope deflection_settlements_side sway
Pérez Gutiérrez María Concepción
 
Ae1 20 21_test 2
Ae1 20 21_test 2Ae1 20 21_test 2
Ae1 20 21_class 3_09_29_statically indeterminate
Ae1 20 21_class 3_09_29_statically indeterminateAe1 20 21_class 3_09_29_statically indeterminate
Ae1 20 21_class 3_09_29_statically indeterminate
Pérez Gutiérrez María Concepción
 
Ae1 21 22_test 2_slope deflection_1
Ae1 21 22_test 2_slope deflection_1Ae1 21 22_test 2_slope deflection_1
Ae1 21 22_test 2_slope deflection_1
Pérez Gutiérrez María Concepción
 
Ae1 21 22_sb_s_frame with and without cantilevers
Ae1 21 22_sb_s_frame with and without cantileversAe1 21 22_sb_s_frame with and without cantilevers
Ae1 21 22_sb_s_frame with and without cantilevers
Pérez Gutiérrez María Concepción
 
Ae1 20 21_class 5_10_16
Ae1 20 21_class 5_10_16Ae1 20 21_class 5_10_16
Ae1 20 21_class 5_10_16
Pérez Gutiérrez María Concepción
 
Ae1 21 22_class 0_structural models
Ae1 21 22_class 0_structural modelsAe1 21 22_class 0_structural models
Ae1 21 22_class 0_structural models
Pérez Gutiérrez María Concepción
 
Ae1 21 22_class 0_07_09_21
Ae1 21 22_class 0_07_09_21Ae1 21 22_class 0_07_09_21
Ae1 21 22_class 0_07_09_21
Pérez Gutiérrez María Concepción
 

What's hot (20)

Ae1 1920 class 4_10_03
Ae1 1920 class 4_10_03Ae1 1920 class 4_10_03
Ae1 1920 class 4_10_03
 
Ae1 1920 class 5_10_8
Ae1 1920 class 5_10_8Ae1 1920 class 5_10_8
Ae1 1920 class 5_10_8
 
Ae1 21 22_class 3_statically indeterminate_class
Ae1 21 22_class 3_statically indeterminate_classAe1 21 22_class 3_statically indeterminate_class
Ae1 21 22_class 3_statically indeterminate_class
 
Ae1 1920 class 3_09_13
Ae1 1920 class 3_09_13Ae1 1920 class 3_09_13
Ae1 1920 class 3_09_13
 
Ae1 21 22_class 7_slope deflection_side sway
Ae1 21 22_class 7_slope deflection_side swayAe1 21 22_class 7_slope deflection_side sway
Ae1 21 22_class 7_slope deflection_side sway
 
Ae1 19 20_2_test 2
Ae1 19 20_2_test 2Ae1 19 20_2_test 2
Ae1 19 20_2_test 2
 
Ae1 19 20_class 2_09_10
Ae1 19 20_class 2_09_10Ae1 19 20_class 2_09_10
Ae1 19 20_class 2_09_10
 
Ae1 21 22_class 8_matrix
Ae1 21 22_class 8_matrixAe1 21 22_class 8_matrix
Ae1 21 22_class 8_matrix
 
Ae1 19 20_1_beam with cantilvers
Ae1 19 20_1_beam with cantilversAe1 19 20_1_beam with cantilvers
Ae1 19 20_1_beam with cantilvers
 
Ae1 19 20_2_test 1
Ae1 19 20_2_test 1Ae1 19 20_2_test 1
Ae1 19 20_2_test 1
 
Ae1 21 22_class 2_statically determinate systems_examples
Ae1 21 22_class 2_statically determinate systems_examplesAe1 21 22_class 2_statically determinate systems_examples
Ae1 21 22_class 2_statically determinate systems_examples
 
Ae1 20 21_class 7_slope deflection_side sway
Ae1 20 21_class 7_slope deflection_side swayAe1 20 21_class 7_slope deflection_side sway
Ae1 20 21_class 7_slope deflection_side sway
 
Ae1 21 22_sb_s_semi frames_slope deflection_settlements_side sway
Ae1 21 22_sb_s_semi frames_slope deflection_settlements_side swayAe1 21 22_sb_s_semi frames_slope deflection_settlements_side sway
Ae1 21 22_sb_s_semi frames_slope deflection_settlements_side sway
 
Ae1 20 21_test 2
Ae1 20 21_test 2Ae1 20 21_test 2
Ae1 20 21_test 2
 
Ae1 20 21_class 3_09_29_statically indeterminate
Ae1 20 21_class 3_09_29_statically indeterminateAe1 20 21_class 3_09_29_statically indeterminate
Ae1 20 21_class 3_09_29_statically indeterminate
 
Ae1 21 22_test 2_slope deflection_1
Ae1 21 22_test 2_slope deflection_1Ae1 21 22_test 2_slope deflection_1
Ae1 21 22_test 2_slope deflection_1
 
Ae1 21 22_sb_s_frame with and without cantilevers
Ae1 21 22_sb_s_frame with and without cantileversAe1 21 22_sb_s_frame with and without cantilevers
Ae1 21 22_sb_s_frame with and without cantilevers
 
Ae1 20 21_class 5_10_16
Ae1 20 21_class 5_10_16Ae1 20 21_class 5_10_16
Ae1 20 21_class 5_10_16
 
Ae1 21 22_class 0_structural models
Ae1 21 22_class 0_structural modelsAe1 21 22_class 0_structural models
Ae1 21 22_class 0_structural models
 
Ae1 21 22_class 0_07_09_21
Ae1 21 22_class 0_07_09_21Ae1 21 22_class 0_07_09_21
Ae1 21 22_class 0_07_09_21
 

Similar to Ae1 1718 class 4b_19_10

AE1_22_23_CLASS 9_22_10_20_STATICALLY INDETERMINATE_class 4.pptx
AE1_22_23_CLASS 9_22_10_20_STATICALLY INDETERMINATE_class 4.pptxAE1_22_23_CLASS 9_22_10_20_STATICALLY INDETERMINATE_class 4.pptx
AE1_22_23_CLASS 9_22_10_20_STATICALLY INDETERMINATE_class 4.pptx
Pérez Gutiérrez María Concepción
 
AE1_22_23_CLASS 6_22_10_06_STATICALLY INDETERMINATE_class 4.pptx
AE1_22_23_CLASS 6_22_10_06_STATICALLY INDETERMINATE_class 4.pptxAE1_22_23_CLASS 6_22_10_06_STATICALLY INDETERMINATE_class 4.pptx
AE1_22_23_CLASS 6_22_10_06_STATICALLY INDETERMINATE_class 4.pptx
Pérez Gutiérrez María Concepción
 
Ae1 1718 class 3_09_26
Ae1 1718 class 3_09_26Ae1 1718 class 3_09_26
Ae1 1718 class 3_09_26
Pérez Gutiérrez María Concepción
 
AE1_22_23_CLASS 3_22_09_19_STATICALLY INDETERMINATE_class.pptx
AE1_22_23_CLASS 3_22_09_19_STATICALLY INDETERMINATE_class.pptxAE1_22_23_CLASS 3_22_09_19_STATICALLY INDETERMINATE_class.pptx
AE1_22_23_CLASS 3_22_09_19_STATICALLY INDETERMINATE_class.pptx
Pérez Gutiérrez María Concepción
 
Ae1 1819 class 6_10_03
Ae1 1819 class 6_10_03Ae1 1819 class 6_10_03
Ae1 1819 class 6_10_03
Pérez Gutiérrez María Concepción
 
Ae1 1819 class 1_09_05
Ae1 1819 class 1_09_05Ae1 1819 class 1_09_05
Ae1 1819 class 1_09_05
Pérez Gutiérrez María Concepción
 
Ae1 20 21_class 2_statically determinate systems_examples
Ae1 20 21_class 2_statically determinate systems_examplesAe1 20 21_class 2_statically determinate systems_examples
Ae1 20 21_class 2_statically determinate systems_examples
Pérez Gutiérrez María Concepción
 
Ae1 18 !9_sb_s_frame_inclined supports and cantilever
Ae1 18 !9_sb_s_frame_inclined supports and cantileverAe1 18 !9_sb_s_frame_inclined supports and cantilever
Ae1 18 !9_sb_s_frame_inclined supports and cantilever
Pérez Gutiérrez María Concepción
 
Ae1 1819 class 7_10_10
Ae1 1819 class 7_10_10Ae1 1819 class 7_10_10
Ae1 1819 class 7_10_10
Pérez Gutiérrez María Concepción
 
AE1_22_23_CLASS 2_22_09_15_STATICALLY DETERMINATE SYSTEMS_EXAMPLES.pptx
AE1_22_23_CLASS 2_22_09_15_STATICALLY DETERMINATE SYSTEMS_EXAMPLES.pptxAE1_22_23_CLASS 2_22_09_15_STATICALLY DETERMINATE SYSTEMS_EXAMPLES.pptx
AE1_22_23_CLASS 2_22_09_15_STATICALLY DETERMINATE SYSTEMS_EXAMPLES.pptx
Pérez Gutiérrez María Concepción
 
Ae1 21 22_class 5_10_08_slope deflection_2
Ae1 21 22_class 5_10_08_slope deflection_2Ae1 21 22_class 5_10_08_slope deflection_2
Ae1 21 22_class 5_10_08_slope deflection_2
Pérez Gutiérrez María Concepción
 
Ae1 17 18_class 0_07_09_17
Ae1 17 18_class 0_07_09_17Ae1 17 18_class 0_07_09_17
Ae1 17 18_class 0_07_09_17
Pérez Gutiérrez María Concepción
 
AE1_22_23_CLASS 3_22_09_22_STATICALLY INDETERMINATE_class 2.pptx
AE1_22_23_CLASS 3_22_09_22_STATICALLY INDETERMINATE_class 2.pptxAE1_22_23_CLASS 3_22_09_22_STATICALLY INDETERMINATE_class 2.pptx
AE1_22_23_CLASS 3_22_09_22_STATICALLY INDETERMINATE_class 2.pptx
Pérez Gutiérrez María Concepción
 
Ae1 1920 class 1_09_06
Ae1 1920 class 1_09_06Ae1 1920 class 1_09_06
Ae1 1920 class 1_09_06
Pérez Gutiérrez María Concepción
 
Ae1 20 21_class 0_18_09_20
Ae1 20 21_class 0_18_09_20Ae1 20 21_class 0_18_09_20
Ae1 20 21_class 0_18_09_20
Pérez Gutiérrez María Concepción
 
AE1_18_19_class 0
AE1_18_19_class 0AE1_18_19_class 0
Ae1 1718 class 3b_09_28
Ae1 1718 class 3b_09_28Ae1 1718 class 3b_09_28
Ae1 1718 class 3b_09_28
Pérez Gutiérrez María Concepción
 
Ae1 20 21_class 1_structural models
Ae1 20 21_class 1_structural modelsAe1 20 21_class 1_structural models
Ae1 20 21_class 1_structural models
Pérez Gutiérrez María Concepción
 
Ae1 1819 class 2_09_12
Ae1 1819 class 2_09_12Ae1 1819 class 2_09_12
Ae1 1819 class 2_09_12
Pérez Gutiérrez María Concepción
 

Similar to Ae1 1718 class 4b_19_10 (19)

AE1_22_23_CLASS 9_22_10_20_STATICALLY INDETERMINATE_class 4.pptx
AE1_22_23_CLASS 9_22_10_20_STATICALLY INDETERMINATE_class 4.pptxAE1_22_23_CLASS 9_22_10_20_STATICALLY INDETERMINATE_class 4.pptx
AE1_22_23_CLASS 9_22_10_20_STATICALLY INDETERMINATE_class 4.pptx
 
AE1_22_23_CLASS 6_22_10_06_STATICALLY INDETERMINATE_class 4.pptx
AE1_22_23_CLASS 6_22_10_06_STATICALLY INDETERMINATE_class 4.pptxAE1_22_23_CLASS 6_22_10_06_STATICALLY INDETERMINATE_class 4.pptx
AE1_22_23_CLASS 6_22_10_06_STATICALLY INDETERMINATE_class 4.pptx
 
Ae1 1718 class 3_09_26
Ae1 1718 class 3_09_26Ae1 1718 class 3_09_26
Ae1 1718 class 3_09_26
 
AE1_22_23_CLASS 3_22_09_19_STATICALLY INDETERMINATE_class.pptx
AE1_22_23_CLASS 3_22_09_19_STATICALLY INDETERMINATE_class.pptxAE1_22_23_CLASS 3_22_09_19_STATICALLY INDETERMINATE_class.pptx
AE1_22_23_CLASS 3_22_09_19_STATICALLY INDETERMINATE_class.pptx
 
Ae1 1819 class 6_10_03
Ae1 1819 class 6_10_03Ae1 1819 class 6_10_03
Ae1 1819 class 6_10_03
 
Ae1 1819 class 1_09_05
Ae1 1819 class 1_09_05Ae1 1819 class 1_09_05
Ae1 1819 class 1_09_05
 
Ae1 20 21_class 2_statically determinate systems_examples
Ae1 20 21_class 2_statically determinate systems_examplesAe1 20 21_class 2_statically determinate systems_examples
Ae1 20 21_class 2_statically determinate systems_examples
 
Ae1 18 !9_sb_s_frame_inclined supports and cantilever
Ae1 18 !9_sb_s_frame_inclined supports and cantileverAe1 18 !9_sb_s_frame_inclined supports and cantilever
Ae1 18 !9_sb_s_frame_inclined supports and cantilever
 
Ae1 1819 class 7_10_10
Ae1 1819 class 7_10_10Ae1 1819 class 7_10_10
Ae1 1819 class 7_10_10
 
AE1_22_23_CLASS 2_22_09_15_STATICALLY DETERMINATE SYSTEMS_EXAMPLES.pptx
AE1_22_23_CLASS 2_22_09_15_STATICALLY DETERMINATE SYSTEMS_EXAMPLES.pptxAE1_22_23_CLASS 2_22_09_15_STATICALLY DETERMINATE SYSTEMS_EXAMPLES.pptx
AE1_22_23_CLASS 2_22_09_15_STATICALLY DETERMINATE SYSTEMS_EXAMPLES.pptx
 
Ae1 21 22_class 5_10_08_slope deflection_2
Ae1 21 22_class 5_10_08_slope deflection_2Ae1 21 22_class 5_10_08_slope deflection_2
Ae1 21 22_class 5_10_08_slope deflection_2
 
Ae1 17 18_class 0_07_09_17
Ae1 17 18_class 0_07_09_17Ae1 17 18_class 0_07_09_17
Ae1 17 18_class 0_07_09_17
 
AE1_22_23_CLASS 3_22_09_22_STATICALLY INDETERMINATE_class 2.pptx
AE1_22_23_CLASS 3_22_09_22_STATICALLY INDETERMINATE_class 2.pptxAE1_22_23_CLASS 3_22_09_22_STATICALLY INDETERMINATE_class 2.pptx
AE1_22_23_CLASS 3_22_09_22_STATICALLY INDETERMINATE_class 2.pptx
 
Ae1 1920 class 1_09_06
Ae1 1920 class 1_09_06Ae1 1920 class 1_09_06
Ae1 1920 class 1_09_06
 
Ae1 20 21_class 0_18_09_20
Ae1 20 21_class 0_18_09_20Ae1 20 21_class 0_18_09_20
Ae1 20 21_class 0_18_09_20
 
AE1_18_19_class 0
AE1_18_19_class 0AE1_18_19_class 0
AE1_18_19_class 0
 
Ae1 1718 class 3b_09_28
Ae1 1718 class 3b_09_28Ae1 1718 class 3b_09_28
Ae1 1718 class 3b_09_28
 
Ae1 20 21_class 1_structural models
Ae1 20 21_class 1_structural modelsAe1 20 21_class 1_structural models
Ae1 20 21_class 1_structural models
 
Ae1 1819 class 2_09_12
Ae1 1819 class 2_09_12Ae1 1819 class 2_09_12
Ae1 1819 class 2_09_12
 

More from Pérez Gutiérrez María Concepción

FM1_geo_1_22_12_12.pptx
FM1_geo_1_22_12_12.pptxFM1_geo_1_22_12_12.pptx
FM1_geo_1_22_12_12.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_22_11_29.pptx
FM1_geo_1_22_11_29.pptxFM1_geo_1_22_11_29.pptx
FM1_geo_1_22_11_29.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_22_11_22.pptx
FM1_geo_1_22_11_22.pptxFM1_geo_1_22_11_22.pptx
FM1_geo_1_22_11_22.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_24_11_15.pptx
FM1_geo_1_24_11_15.pptxFM1_geo_1_24_11_15.pptx
FM1_geo_1_24_11_15.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_24_11_14.pptx
FM1_geo_1_24_11_14.pptxFM1_geo_1_24_11_14.pptx
FM1_geo_1_24_11_14.pptx
Pérez Gutiérrez María Concepción
 
AE1_22_23_CLASS_MATRIX.pptx
AE1_22_23_CLASS_MATRIX.pptxAE1_22_23_CLASS_MATRIX.pptx
AE1_22_23_CLASS_MATRIX.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_24_11_8.pptx
FM1_geo_1_24_11_8.pptxFM1_geo_1_24_11_8.pptx
FM1_geo_1_24_11_8.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_24_11_7.pptx
FM1_geo_1_24_11_7.pptxFM1_geo_1_24_11_7.pptx
FM1_geo_1_24_11_7.pptx
Pérez Gutiérrez María Concepción
 
AE1_21_22_TEST 3_SLOPE DEFLECTION_2.pptx
AE1_21_22_TEST 3_SLOPE DEFLECTION_2.pptxAE1_21_22_TEST 3_SLOPE DEFLECTION_2.pptx
AE1_21_22_TEST 3_SLOPE DEFLECTION_2.pptx
Pérez Gutiérrez María Concepción
 
AE1_11_22_frame competition.pptx
AE1_11_22_frame competition.pptxAE1_11_22_frame competition.pptx
AE1_11_22_frame competition.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_24_10_25.pptx
FM1_geo_1_24_10_25.pptxFM1_geo_1_24_10_25.pptx
FM1_geo_1_24_10_25.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_24_10_24.pptx
FM1_geo_1_24_10_24.pptxFM1_geo_1_24_10_24.pptx
FM1_geo_1_24_10_24.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_22_10_18.pptx
FM1_geo_1_22_10_18.pptxFM1_geo_1_22_10_18.pptx
FM1_geo_1_22_10_18.pptx
Pérez Gutiérrez María Concepción
 
FM1_geo_1_22_10_17.pptx
FM1_geo_1_22_10_17.pptxFM1_geo_1_22_10_17.pptx
FM1_geo_1_22_10_17.pptx
Pérez Gutiérrez María Concepción
 
AE1_21_22_SbS_two span_inclined supports frame_slope deflection_.pptx
AE1_21_22_SbS_two span_inclined supports frame_slope deflection_.pptxAE1_21_22_SbS_two span_inclined supports frame_slope deflection_.pptx
AE1_21_22_SbS_two span_inclined supports frame_slope deflection_.pptx
Pérez Gutiérrez María Concepción
 

More from Pérez Gutiérrez María Concepción (20)

FM1_geo_1_22_12_13.pptx
FM1_geo_1_22_12_13.pptxFM1_geo_1_22_12_13.pptx
FM1_geo_1_22_12_13.pptx
 
FM1_geo_1_22_12_12.pptx
FM1_geo_1_22_12_12.pptxFM1_geo_1_22_12_12.pptx
FM1_geo_1_22_12_12.pptx
 
FM1_geo_1_22_11_29.pptx
FM1_geo_1_22_11_29.pptxFM1_geo_1_22_11_29.pptx
FM1_geo_1_22_11_29.pptx
 
FM1_geo_1_22_11_29.pptx
FM1_geo_1_22_11_29.pptxFM1_geo_1_22_11_29.pptx
FM1_geo_1_22_11_29.pptx
 
FM1_geo_1_22_11_28.pptx
FM1_geo_1_22_11_28.pptxFM1_geo_1_22_11_28.pptx
FM1_geo_1_22_11_28.pptx
 
FM1_geo_1_22_11_22.pptx
FM1_geo_1_22_11_22.pptxFM1_geo_1_22_11_22.pptx
FM1_geo_1_22_11_22.pptx
 
FM1_geo_1_22_11_21.pptx
FM1_geo_1_22_11_21.pptxFM1_geo_1_22_11_21.pptx
FM1_geo_1_22_11_21.pptx
 
FM1_geo_1_22_11_21.pptx
FM1_geo_1_22_11_21.pptxFM1_geo_1_22_11_21.pptx
FM1_geo_1_22_11_21.pptx
 
FM1_geo_1_24_11_15.pptx
FM1_geo_1_24_11_15.pptxFM1_geo_1_24_11_15.pptx
FM1_geo_1_24_11_15.pptx
 
FM1_geo_1_24_11_14.pptx
FM1_geo_1_24_11_14.pptxFM1_geo_1_24_11_14.pptx
FM1_geo_1_24_11_14.pptx
 
AE1_22_23_CLASS_MATRIX.pptx
AE1_22_23_CLASS_MATRIX.pptxAE1_22_23_CLASS_MATRIX.pptx
AE1_22_23_CLASS_MATRIX.pptx
 
FM1_geo_1_24_11_8.pptx
FM1_geo_1_24_11_8.pptxFM1_geo_1_24_11_8.pptx
FM1_geo_1_24_11_8.pptx
 
FM1_geo_1_24_11_7.pptx
FM1_geo_1_24_11_7.pptxFM1_geo_1_24_11_7.pptx
FM1_geo_1_24_11_7.pptx
 
AE1_21_22_TEST 3_SLOPE DEFLECTION_2.pptx
AE1_21_22_TEST 3_SLOPE DEFLECTION_2.pptxAE1_21_22_TEST 3_SLOPE DEFLECTION_2.pptx
AE1_21_22_TEST 3_SLOPE DEFLECTION_2.pptx
 
AE1_11_22_frame competition.pptx
AE1_11_22_frame competition.pptxAE1_11_22_frame competition.pptx
AE1_11_22_frame competition.pptx
 
FM1_geo_1_24_10_25.pptx
FM1_geo_1_24_10_25.pptxFM1_geo_1_24_10_25.pptx
FM1_geo_1_24_10_25.pptx
 
FM1_geo_1_24_10_24.pptx
FM1_geo_1_24_10_24.pptxFM1_geo_1_24_10_24.pptx
FM1_geo_1_24_10_24.pptx
 
FM1_geo_1_22_10_18.pptx
FM1_geo_1_22_10_18.pptxFM1_geo_1_22_10_18.pptx
FM1_geo_1_22_10_18.pptx
 
FM1_geo_1_22_10_17.pptx
FM1_geo_1_22_10_17.pptxFM1_geo_1_22_10_17.pptx
FM1_geo_1_22_10_17.pptx
 
AE1_21_22_SbS_two span_inclined supports frame_slope deflection_.pptx
AE1_21_22_SbS_two span_inclined supports frame_slope deflection_.pptxAE1_21_22_SbS_two span_inclined supports frame_slope deflection_.pptx
AE1_21_22_SbS_two span_inclined supports frame_slope deflection_.pptx
 

Recently uploaded

Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
AJAYKUMARPUND1
 
Vaccine management system project report documentation..pdf
Vaccine management system project report documentation..pdfVaccine management system project report documentation..pdf
Vaccine management system project report documentation..pdf
Kamal Acharya
 
Cosmetic shop management system project report.pdf
Cosmetic shop management system project report.pdfCosmetic shop management system project report.pdf
Cosmetic shop management system project report.pdf
Kamal Acharya
 
LIGA(E)11111111111111111111111111111111111111111.ppt
LIGA(E)11111111111111111111111111111111111111111.pptLIGA(E)11111111111111111111111111111111111111111.ppt
LIGA(E)11111111111111111111111111111111111111111.ppt
ssuser9bd3ba
 
The role of big data in decision making.
The role of big data in decision making.The role of big data in decision making.
The role of big data in decision making.
ankuprajapati0525
 
MCQ Soil mechanics questions (Soil shear strength).pdf
MCQ Soil mechanics questions (Soil shear strength).pdfMCQ Soil mechanics questions (Soil shear strength).pdf
MCQ Soil mechanics questions (Soil shear strength).pdf
Osamah Alsalih
 
Nuclear Power Economics and Structuring 2024
Nuclear Power Economics and Structuring 2024Nuclear Power Economics and Structuring 2024
Nuclear Power Economics and Structuring 2024
Massimo Talia
 
power quality voltage fluctuation UNIT - I.pptx
power quality voltage fluctuation UNIT - I.pptxpower quality voltage fluctuation UNIT - I.pptx
power quality voltage fluctuation UNIT - I.pptx
ViniHema
 
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdfHybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
fxintegritypublishin
 
addressing modes in computer architecture
addressing modes  in computer architectureaddressing modes  in computer architecture
addressing modes in computer architecture
ShahidSultan24
 
Planning Of Procurement o different goods and services
Planning Of Procurement o different goods and servicesPlanning Of Procurement o different goods and services
Planning Of Procurement o different goods and services
JoytuBarua2
 
ASME IX(9) 2007 Full Version .pdf
ASME IX(9)  2007 Full Version       .pdfASME IX(9)  2007 Full Version       .pdf
ASME IX(9) 2007 Full Version .pdf
AhmedHussein950959
 
Quality defects in TMT Bars, Possible causes and Potential Solutions.
Quality defects in TMT Bars, Possible causes and Potential Solutions.Quality defects in TMT Bars, Possible causes and Potential Solutions.
Quality defects in TMT Bars, Possible causes and Potential Solutions.
PrashantGoswami42
 
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptx
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxCFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptx
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptx
R&R Consult
 
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
MdTanvirMahtab2
 
Student information management system project report ii.pdf
Student information management system project report ii.pdfStudent information management system project report ii.pdf
Student information management system project report ii.pdf
Kamal Acharya
 
Event Management System Vb Net Project Report.pdf
Event Management System Vb Net  Project Report.pdfEvent Management System Vb Net  Project Report.pdf
Event Management System Vb Net Project Report.pdf
Kamal Acharya
 
Gen AI Study Jams _ For the GDSC Leads in India.pdf
Gen AI Study Jams _ For the GDSC Leads in India.pdfGen AI Study Jams _ For the GDSC Leads in India.pdf
Gen AI Study Jams _ For the GDSC Leads in India.pdf
gdsczhcet
 
ethical hacking-mobile hacking methods.ppt
ethical hacking-mobile hacking methods.pptethical hacking-mobile hacking methods.ppt
ethical hacking-mobile hacking methods.ppt
Jayaprasanna4
 
Automobile Management System Project Report.pdf
Automobile Management System Project Report.pdfAutomobile Management System Project Report.pdf
Automobile Management System Project Report.pdf
Kamal Acharya
 

Recently uploaded (20)

Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
Pile Foundation by Venkatesh Taduvai (Sub Geotechnical Engineering II)-conver...
 
Vaccine management system project report documentation..pdf
Vaccine management system project report documentation..pdfVaccine management system project report documentation..pdf
Vaccine management system project report documentation..pdf
 
Cosmetic shop management system project report.pdf
Cosmetic shop management system project report.pdfCosmetic shop management system project report.pdf
Cosmetic shop management system project report.pdf
 
LIGA(E)11111111111111111111111111111111111111111.ppt
LIGA(E)11111111111111111111111111111111111111111.pptLIGA(E)11111111111111111111111111111111111111111.ppt
LIGA(E)11111111111111111111111111111111111111111.ppt
 
The role of big data in decision making.
The role of big data in decision making.The role of big data in decision making.
The role of big data in decision making.
 
MCQ Soil mechanics questions (Soil shear strength).pdf
MCQ Soil mechanics questions (Soil shear strength).pdfMCQ Soil mechanics questions (Soil shear strength).pdf
MCQ Soil mechanics questions (Soil shear strength).pdf
 
Nuclear Power Economics and Structuring 2024
Nuclear Power Economics and Structuring 2024Nuclear Power Economics and Structuring 2024
Nuclear Power Economics and Structuring 2024
 
power quality voltage fluctuation UNIT - I.pptx
power quality voltage fluctuation UNIT - I.pptxpower quality voltage fluctuation UNIT - I.pptx
power quality voltage fluctuation UNIT - I.pptx
 
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdfHybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
Hybrid optimization of pumped hydro system and solar- Engr. Abdul-Azeez.pdf
 
addressing modes in computer architecture
addressing modes  in computer architectureaddressing modes  in computer architecture
addressing modes in computer architecture
 
Planning Of Procurement o different goods and services
Planning Of Procurement o different goods and servicesPlanning Of Procurement o different goods and services
Planning Of Procurement o different goods and services
 
ASME IX(9) 2007 Full Version .pdf
ASME IX(9)  2007 Full Version       .pdfASME IX(9)  2007 Full Version       .pdf
ASME IX(9) 2007 Full Version .pdf
 
Quality defects in TMT Bars, Possible causes and Potential Solutions.
Quality defects in TMT Bars, Possible causes and Potential Solutions.Quality defects in TMT Bars, Possible causes and Potential Solutions.
Quality defects in TMT Bars, Possible causes and Potential Solutions.
 
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptx
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxCFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptx
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptx
 
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
Industrial Training at Shahjalal Fertilizer Company Limited (SFCL)
 
Student information management system project report ii.pdf
Student information management system project report ii.pdfStudent information management system project report ii.pdf
Student information management system project report ii.pdf
 
Event Management System Vb Net Project Report.pdf
Event Management System Vb Net  Project Report.pdfEvent Management System Vb Net  Project Report.pdf
Event Management System Vb Net Project Report.pdf
 
Gen AI Study Jams _ For the GDSC Leads in India.pdf
Gen AI Study Jams _ For the GDSC Leads in India.pdfGen AI Study Jams _ For the GDSC Leads in India.pdf
Gen AI Study Jams _ For the GDSC Leads in India.pdf
 
ethical hacking-mobile hacking methods.ppt
ethical hacking-mobile hacking methods.pptethical hacking-mobile hacking methods.ppt
ethical hacking-mobile hacking methods.ppt
 
Automobile Management System Project Report.pdf
Automobile Management System Project Report.pdfAutomobile Management System Project Report.pdf
Automobile Management System Project Report.pdf
 

Ae1 1718 class 4b_19_10

  • 1. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es STRUCTURAL ANALYSIS I Degree in Architecture Year 3 Term 1 EPS USPCEU
  • 2. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es STATICALLY INDETERMINATE STRUCTURES. SLOPE DEFLECTION METHOD TEST 3_year 16_17 SLOPE DEFLECTION METHOD. NON-SWAY FRAME
  • 3. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es CAN YOU SOLVE ALL OF THEM? HOW MANY DEGREES OF FREEDOM CAN YOU FIND IN EACH FRAME?
  • 4. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es WHAT ABOUT VERTICAL REACTION FORCES? AND WHAT ABOUT HORIZONTAL REACTION FORCES?
  • 5. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es WILL BENDING MOMENTS BE EQUAL IN FRAMES 1 AND 2? WILL BENDING MOMENTS BE EQUAL IN FRAMES 3 AN 4?
  • 6. STRUCTURAL 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?
  • 7. STRUCTURAL 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)
  • 8. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b LOAD ALONG THE BARS EFFECT
  • 9. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b ROTATION EFFECT
  • 10. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b DISPLACEMENT EFFECT
  • 11. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b ROTATION EFFECT
  • 12. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b SIMPLIFIED FORMULAS USED WHEN ONE OF THE BAR END MOMENTS IS ZERO
  • 13. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b SIMPLIFIED FORMULAS USED WHEN ONE OF THE BAR END MOMENTS IS ZERO BE CAREFUL! WE SHOULD BE CONSISTANT!!! IF WE CONSIDER M=0 WHEN COMPUTING ROTATION EFFECTS WE SHOULD ALSO CONSIDER M=0 WHEN COMPUTING LOADS EFFECT AND DISPLACEMENTS EFFECTS
  • 14. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b NO END MOMENT ZERO
  • 15. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b ONE END MOMENT ZERO
  • 16. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 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)
  • 17. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es SLOPE DEFLECTION METHOD STEP BY STEP 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!
  • 18. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es SLOPE DEFLECTION METHOD STEP BY STEP 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.
  • 19. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es SLOPE DEFLECTION METHOD STEP BY STEP ROTATIONS and DISPLACEMENTS END MOMENTS SHEAR FORCES AXIAL FORCES
  • 20. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 1.- DEGREES OF FREEDOM?
  • 21. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS
  • 22. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS
  • 23. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 2.- FIXED END MOMENTS. EFFECT OF THE LOAD APPLIED ALONG THE BARS
  • 24. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE EFFECT OF THE ROTATIONS cv c v c v
  • 25. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE EFFECT OF THE ROTATIONS
  • 26. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 3.- FREE ENDS ROTATION. WE MAKE JOINTS C AND D ROTATE AND ANALYZE THE EFFECT OF THE ROTATIONS
  • 27. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 4.- DISPLACEMENTS: NOT IN THIS FRAME
  • 28. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 5 and 6.- EQUILIBRIUM EQUATION 𝑴 𝒄 = 𝟎
  • 29. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 7.- END MOMENTS load rotation load load rotation rotation rotationload
  • 30. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 7.- END MOMENTS
  • 31. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 8.- SHEAR FORCES
  • 32. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 10.- BENDING MOMENT DIAGRAM
  • 33. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 10.- SHEAR FORCE DIAGRAM
  • 34. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 9.- AXIAL FORCES JOINT C EQUILIBRIUM
  • 35. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 9.- AXIAL FORCES
  • 36. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 11.- DEFORMED SHAPE
  • 37. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es -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
  • 38. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es 1,33 mm -2,00 mm 11.- VERTICAL DISPLCAMENT AT THE END OF THE CANTILEVER EFFECT OF THE LOAD EFFECT OF THE ROTATION
  • 39. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4b cperez.eps@ceu.es federico.prietomunoz@ceu.es
  • 40. STRUCTURAL ANALYSIS I 2017/2018 CLASS 4 cperez.eps@ceu.es federico.prietomunoz@ceu.es