1. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
cperez.eps@ceu.es
molina.eps@ceu.es
Hipódromo de la Zarzuela. Madrid 1931. Archiches y Domínguaz. Eduardo Torroja.
Assignment 1 year 18/19
STATICALLY DETERMINATE BEAMS AND FRAMES
DISPLACEMENTS
7. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
real bars elongation
Δ𝐿 =
𝑁𝐿
𝐸𝐴
It gives us information
about the contribution of
each member to the
displacement we want to
calculate
vC= 𝑁∗ 𝑥
𝑁𝐿
𝐸𝐴
=
−23,48𝑃𝑎
𝐸𝐴
8. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
It gives us information
about the contribution of
each member to the
displacement we want to
calculate
vC = 𝑁∗ 𝑥
𝑁𝐿
𝐸𝐴
=
14,48𝑃𝑎
𝐸𝐴
real bars elongation
Δ𝐿 =
𝑁𝐿
𝐸𝐴
20. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
REMEMBER!
WE ONLY CONSIDER MOVEMENTS PRODUCED BY BENDING
MOMENTS. WE NEGLECT SHEAR FORCE AND AXIAL FORCE
DEFORMATIONS. WE ASSUME BARS ARE INEXTENSIBLE
42. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
TO CALCULATE THE HORIZONTAL DISPLACEMENT AT THE ROLLER WE MUST USE
AN AUXILIARY SYSTEM
CAN THIS SYSTEM BE THE SAME FOR EVERY TRUSS?
53. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
TO CALCULATE THE VERTICAL DISPLACEMENT AT C…
WHICH EFFECTS DO WE HAVE TO CONSIDER?
BEAM 6
WE MUST CONSIDER SAME AS BEAM (5)
PLUS THE EFFECT OF THE CABLE ELONGATION
55. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
BEAM 6
WE WOULD GET SAME RESULT IF WE APPLY UNIT LOAD METHOD
WATCH OUT!!!!!
WE SHOULD CONSIDER
THE BENDING
MOMENTS OF THE
BEAM AND THE AXIAL
FORCE IN THE CABLE!
70. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
VERTICAL DISPLACEMENT AT F
ONLY THE CABLE AXIAL FORCE AFFECTS IT
vF = N x L / EA
vF = 3P x 6a / 65971,5
F goes up
vF varies from 1,81 mm to 3,8 mm
71. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
HORIZONTAL DISPLACEMENT AT G
ONLY THE COLUMN BG BENDING MOMENT AFFECTS IT
uG = 4,5qa x (6a + 4 x 4,5a + 3a)/(6x 52857) x 3a
uG varies between 11,49 and 55,37 mm
72. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
HORIZONTAL DISPLACEMENT AT D
ONLY THE COLUMN BG BENDING MOMENT AFFECTS IT
uD = 4,5qa2 x (3a + 4 x 1,5a + 0)/(6x 52857) x 3a
uD varies between 3,83 and 18,46 mm
73. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
VERTICAL DISPLACEMENT AT D
THE COLUMN BG AND THE BEAM CD BENDING MOMENTS AFFECTS IT
vD = 3qa2 + 4 x 3a + 3a)/(6x 52857) x 3a +
(4,5qa2 x 3a + 4 x 1,125qa2 x 1,5a + 0)/(6x11970) x 3a
vD varies between -16,1 and -77,7 mm
74. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
VERTICAL DISPLACEMENT AT J
THE TRUSS AND THE CABLE AXIAL FORCE AFFECT IT
vJ = S (N* x N x L / EA)for each bar + P x (-3) /65951
vJ varies between -12,21 and -25,67 mm
75. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
VERTICAL DISPLACEMENT AT I
THE TRUSS AND THE CABLE AXIAL FORCE AFFECT IT
vJ = S (N* x N x L / EA)for each bar + P x (+2) /65951
vJ varies between 4,81 and 10,11 mm
76. cperez.eps@ceu.es
molina.eps@ceu.es
STRUCTURAL ANALYSIS I
DEGREE IN ARCHITECTURE
Year 3 Term 1
STATICALLY DETERMINATE SYSTEMS
REMEMBER!
IN BEAMS A COLUMNS WE ONLY CONSIDER MOVEMENTS
PRODUCED BY BENDING MOMENTS. WE NEGLECT SHEAR
FORCE AND AXIAL FORCE DEFORMATIONS. WE ASSUME BARS
ARE INEXTENSIBLE
UNLESS CABLES OR TRUSSES ARE INVOLVED