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STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
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 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
TEST 1:
TRUSSES 1, 2, 3 and 4
BEAMS 5 and 6
STATICALLY INDETERMINATE STRUCTURES
COMPATIBILITY METHOD
ASSIGNMENT 3
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
ARE ALL OF THEM STATICALLY DETERMINATE?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
REMEMBER:
THE LOAD FOLLOWS THE SHORTEST WAY
TO REACH THE GROUND
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
WHICH BARS ARE GOING TO WORK IN EACH TRUSS?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
WHICH BARS ARE GOING TO WORK IN EACH TRUSS?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
WHICH BARS ARE GOING TO WORK IN EACH TRUSS?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
AXIAL FORCES
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
DO THESE RESLTS MAKE SENSE?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
CAN WE APPLY THE SUPERPOSITION PRINCIPLE?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
TO CALCULATE THE HORIZONTAL DISPLACEMENT AT THE ROLLER WE MUST USE
AN AUXILIARY SYSTEM
CAN THIS SYSTEM BE THE SAME FOR EVERY TRUSS?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
CAN WE APPLY THE SUPERPOSITION PRINCIPLE?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
SIMILARITIES AND DIFFERENCES?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
REACTION FORCES
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
BENDING MOMENTS
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
DISPLACEMENT AT THE END OF THE CANTILEVER?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
REMEMBER!
WE ONLY CONSIDER MOVEMENTS PRODUCED BY BENDING
MOMENTS. WE NEGLECT SHEAR FORCE AND AXIAL FORCE
DEFORMATIONS. WE ASSUME BARS ARE INEXTENSIBLE
UNLESS CABLES ARE INVOLVED
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
DISPLACEMENT AT THE END OF THE CANTILEVER?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
ROTATION AT B IN (5)
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
DISPLACEMENT AT C IN (5)
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
DISPLACEMENT AT C IN (6) UNIT LOAD METHOD
P* x uC = N∗𝑥 𝑁 𝐿 /𝐸𝐴
UNIT LOAD METHOD
P* x uC =
𝑀⋅𝑀∗
𝐸𝐼
ⅆ𝑥
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
DISPLACEMENT AT C IN (6) UNIT LOAD METHOD
P* x uC = N∗𝑥 𝑁 𝐿 /𝐸𝐴
𝑢𝐶 =
𝑀1 ∙ 𝑀1
∗
+ 4𝑀2 ∙ 𝑀2
∗
+ 𝑀3 ∙ 𝑀3
∗
6𝐸𝐼
𝑥 𝐿
=
4 𝑥7𝑞𝑎2
𝑥1 − 2𝑞𝑎2
𝑥2 𝑥8𝑎
6𝐸𝐼
+
−2𝑞𝑎2
𝑥2 − 4𝑥0,5𝑞𝑎2
𝑥1 𝑥2𝑎
6𝐸𝐼
= 30 qa4
/EI
𝑢𝐶 =
𝑁∙𝑁∗∙𝐿
𝐸𝐴
=
25𝑞𝑎/4∙ −1,25 𝑥 3𝑎
𝐸𝐴
= - 23,44 qa2 /EA
cable
beam
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
BEAM (5) DEFORMED SHAPE
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
BEAM (6) DEFORMED SHAPE
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
2.- STATICALLY INDETERMINATE BEAMS. COMPATIBILITY METHOD.
WHAT HAPPENS WHEN THE BEAM IS STATICALLY INDETERMINATE?
EQUILIBRIUM EQUATIONS ARE NOT ENOUGH TO SOLVE IT
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
WE CAN CONSIDER THE SYSTEM AS AN ADDITION OF TWO STATICALLY DETERMINATE ONES!
DIVIDE TO WIN!!!!
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
DIVIDE TO WIN!!!!
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
WE NEED TO KNOW THE BEAM CROSS SECTION TO CALCULATE THE REACTION FORCES…
IN STATICALLY INDETERMINATE SYSTEMS THE RESULT IS DIFFERENT DEPENDING ON THE
CROSS SECTION DIMENSIONS…
STRUCTURAL ANALYSIS I
2016/2017 CLASS 3
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
2.- STATICALLY INDETERMINATE BEAMS. COMPATIBILITY METHOD.
WHAT HAPPENS WHEN A BEAM IS LINKED WITH A CABLE?
EQUILIBRIUM EQUATIONS ARE NOT ENOUGH TO SOLVE IT
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
2.- STATICALLY INDETERMINATE BEAMS. COMPATIBILITY METHOD.
WHAT HAPPENS WHEN A BEAM IS LINKED WITH A CABLE?
EQUILIBRIUM EQUATIONS ARE NOT ENOUGH TO SOLVE IT
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
WE CAN CONSIDER THE SYSTEM AS AN ADDITION OF TWO STATICALLY DETERMINATE ONES!
DIVIDE TO WIN!!!!
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
Displacement due to q
Displacement due to N
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
vC,q =
5⋅𝑞⋅𝐿4
384𝐸𝐼
vC,N =
𝑁⋅𝐿3
48𝐸𝐼
Displacement due to q
Displacement due to N
Δ𝐿 =
𝑁𝐿
𝐸𝐴
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
Data:
EI (IPE200) = 21000 kN/cm2 ∙ 1940 cm4 = 4074 kNm2
EA (ø20 ) = 210 kN/mm2 ∙ 314,15 mm2 = 65971 kN
vC,q =-
5⋅𝑞⋅𝐿4
384𝐸𝐼
= -0,1309 m
vC,N =
𝑁⋅𝐿3
48𝐸𝐼
= 2,61 x 10−3
N m
Δ𝐿 =
𝑁𝐿
𝐸𝐴
= −4,54 x 10−5 N m
vC,q + vC, N = ∆L
N = 49,16 kN
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
CALCULATE THE VALUE OF THE DISPLACEMENT IN THE MIDDLE OF THE SPAN!!!!!!!
CHECK IF THE RESULT IS CORRECT!!! HOW???
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
WHAT HAPPENS IF WE CONSIDER A ROLLER INSTEAD OF A CABLE?
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
vC,q =
5⋅𝑞⋅𝐿4
384𝐸𝐼
vC,N =
𝑁⋅𝐿3
48𝐸𝐼
vC,q + vC, N = 0
N = 50 kN
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es
STRUCTURAL ANALYSIS I
2017/2018 CLASS 3
cperez.eps@ceu.es
federico.prietomunoz@ceu.es

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