Statics 2017 - Szt courses/2_statics/lecture... · Statics 2017 2 tests: 120+120 points, 1+1...
Transcript of Statics 2017 - Szt courses/2_statics/lecture... · Statics 2017 2 tests: 120+120 points, 1+1...
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Statics 2017
2 tests: 120+120 points, 1+1 replacement
2 HWs: 10+10 points, optional
min requirement for signature: 50% including HW points!
2x90 minutes final exam: minimum 50%
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Study aids:
lecture notes by Gimesy & Laki from opur copy room (K264)
collection of examples: Kőrössi & Laki from opur copy room (K264)
forum: piazza.com
personal consultation: during office hours of Rita Vajk and Peter Varkonyi
[email protected] [email protected]
www.szt.bme.hu
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Statics 2017: Lecture 1
Steps of structural analysis
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1. reality
2. modelling
3. calculation
4. questions and answers
pictures credit: Kollár László: Introduction to str. des. a tartószerkezettervezésbe
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1. Reality is too complicated for analysis
famous example of unexpected complications:Tacoma Narrows Bridge
https://www.youtube.com/watch?v=j-zczJXSxnw
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2. Modeling: simplifies but captures important aspects
- idealized loads:
- idealized supports
- idealized geometry:
cross-section:
Basic values given by standards, You already know about: load combinations, safety factorsMore details: tartószerkezetek Design of loadbearing str.e tárgy
usually we determine it, difficult task to determineMore details: Design of load-bearing str. class in 3rd year
Mec
han
ical
mo
del
of
stru
ctu
re
hinge, roller, fixed support, ....difficult task to choose the right oneMore details: Design of load-bearing str. class in 3rd year
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About idealized geometry
(source: Kollár L. Introduction to str. des. a tartószerkezettervezésbe
p
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About idealized supports
y
y y
xx x
(a) (b)
y
x
(source: Kollár L. Introduction to str. des. a tartószerkezettervezésbe
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- idealized material laws
- more assumptions
cross-section
you may know from physics classes Hooke’s lawMore details: strength of materials 1
Just an example: neglecting the effect of deformations
2. Modeling: simplifies but captures important aspects
- idealized loads:
- idealized supports
- idealized geometry:
Basic values given by standards, You already know about: load combinations, safety factorsMore details: tartószerkezetek Design of loadbearing str.e tárgy
usually we choose it, and you do not have to difficult task to determineMore details: Design of load-bearing str. class in 3rd year
hinge, roller, fixed support, ....difficult task to choose the right oneMore details: Design of load-bearing str. class in 3rd year
Mec
han
ical
mo
del
of
stru
ctu
re
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example: neglecting the effect of deformations
1 N
3 m1 N
3 Nm
1 N
5,5 m
5,5 Nm
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2. A mechanikai modell: kezelhető, de megragadja a lényeget
- idealizált terhek:
- idealizált támaszok
- idealizált geometria:
- idealizált anyagi viselkedés
- egyéb egyszerűsítések
keresztmetszet
Alapértékeket szabvány adja meg, Tanult alapelvek: biztonsági tényező, teherkombinációkRészletesebben: tartószerkezetek Design of loadbearing str.e tárgy
általában megadjuk, helyes választás nehézRészletesebben: tartószerkezetek Design of loadbearing str.e tárgy
csukló, görgő, befogás, ....helyes választás nehézRészletesebben: tartószerkezetek Design of loadbearing str.e tárgy
középiskolából: Hooke törvényRészletesebben: strength of materials 1
Csak egy példa: alakváltozások hatásának elhanyagolása
choice of mechanical model:
most important and most difficult task of an engineer
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3. Calculation
- internal forces
- stress
- support reaction, connection forces
- displacements
- many other: e.g. properties of vibrations, width of cracks
Introduction, staticsStrength 2 (statically indeterminate structures)(Computer-aided design)
statics(Computer-aided design)
strength of materials 1(Computer-aided design)
strength of materials 2Design of loadbearing str.(Computer-aided design)
reinforced concrete,...
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3. Calculation
- internal forces
- stress
- support reaction, connection forces
- displacements
- many other: e.g. properties of vibrations, width of cracks
Introduction, staticsStrength 2 (statically indeterminate structures)(Computer-aided design)
staticsSzerkterv számítógéppel
strength of materials 1(Computer-aided design)
strength of materials 2Design of loadbearing str.(Computer-aided design)
reinforced concrete,...
Calculation
necessary to understand structural behaviour
at this time mostly done by computers
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4. Questions and answers
- Is it useable?
- Is it durable enough?
- Is the structure safe?
e.g. – vibrations are not disturbing- deformations are not disturbing, adjacent building elements
are not damaged,water flows down from roof, etc.- water-tight concrete structure has no cracks
e.g. cracks of reinforced concrete structure are not too wide, otherwise steel bars will corrode.
Global equilibrium? (sliding, turnover, floating,...?)
Strong enogh? (material can bear stresses generated by loads?)
Stable?(see example in video)
Soil strong enough under structure?
Introduction to str. des.
statics+strength of materials 1
strength of materials 2,
Talajmechanika
Dynamicsstrength of materials 2.....
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Global equilibrium...
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The story of Pom-pom s01e02
https://www.youtube.com/watch?v=RlNtE85-k-g
see at 02:50
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he problem of usabilityLondon Millenium Bridge
after 01:15
https://www.youtube.com/watch?v=7GuRPlWnrto
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statics 2017: lecture 1
Summary of previous semester
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vectors: sum, components, scalar product, cross productsystems of linear equations
equilibrium of point
distributed forces, resultant, center of mass
equilibrium of planar body, supports, constraints
loads, load combinations, safety factors
support reactions of simple structures and complex structures
3-hinged structure
statical determinacy
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simple planar structures
- at least 3 support reactions- not a collection of parallel forces- not a collection of forces pointing to a single point
(statically determinate) (statically determinate)(statically indeterminate)
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WRONG!(statically indeterminate
and overdeterminate)
simple planar structures
- at least 3 support reactions- not a collection of parallel forces- not a collection of forces pointing to a single point
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3-hinged structure >> simplest strategy of finding support reactions
𝑒𝑔é𝑠𝑧
𝑀𝐴 = 0
𝐵𝐶
𝑀𝑐 = 0
system of 2 equations, or 2 separate equationsBx, By
A
C
Bit is easy to continue from here
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3-hinged structure >> when does it work?- three hinges should not be collinear
A
C
B
A
C
B
GOOD BAD
(statically determinate)
(statically indeterminateand overdeterminate)
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3-hinged structure >> coping with horizontal support reactions of roofs
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timber slab + roof:no problem
tie beam
!
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modern buildings with functional use of roof:tie beam not possible
timber slab + roof:no problem
tie beam
!
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!
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planar, complex structures>> „stupid” way of finding support reactions
3 equilibrium equations / rigid element2 equilibrium equations / point-like element
system of equations provides unknown support reactions and connection forces
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statical determinacydo the equilibrium equations have a unique solution?
equilibrium equations have exactly 1 solution for any load
if e=u (where e=number of equilibrium equations, u=number of unknown forces and moments) and determinant of the coefficient mat-rix of the equilibrium equations is not 0
statically determinate: just enogh supports, connection to carry loads
statically indeterminate: more than necessary supports, constraints somewhere
statically overdeterminate: less than necessary supports, constraints somewhere
equilibrium equations have >1 solutions for some load
equilibrium equations have no solution for some load
usually not acceptable
not a problem, but we need different strategy to find support reactions > strength of materials 2
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statical determinacy: classification of structures
structures
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determinate
indeterminate overdeterminate
indeterminate and overdeterminate
statical determinacy: classification of structures
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statical determinacy: what is counting equations and unknowns good for?
indeterminate overdeterminate
indeterminate and overdeterminate
határozotte=u
detM ≠0
e=udetM = 0
e < u e > u
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határozatlan túlhatározott
határozatlan és túlhatározott
határozotte=i
detM ≠0
e=idetM = 0
e < i e > i
statical determinacy: examples
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Complex structures >> smart way of finding
support reactions
Next week: