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%

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

vpeter@mit.bme.hu rita.vajk@gmail.com

www.szt.bme.hu

Statics 2017: Lecture 1

Steps of structural analysis

1. reality

2. modelling

3. calculation

4. questions and answers

pictures credit: Kollár László: Introduction to str. des. a tartószerkezettervezésbe

1. Reality is too complicated for analysis

famous example of unexpected complications:Tacoma Narrows Bridge

https://www.youtube.com/watch?v=j-zczJXSxnw

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

About idealized geometry

(source: Kollár L. Introduction to str. des. a tartószerkezettervezésbe

p

About idealized supports

y

y y

xx x

(a) (b)

y

x

(source: Kollár L. Introduction to str. des. a tartószerkezettervezésbe

- 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

example: neglecting the effect of deformations

1 N

3 m1 N

3 Nm

1 N

5,5 m

5,5 Nm

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

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,...

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

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.....

Global equilibrium...

The story of Pom-pom s01e02

https://www.youtube.com/watch?v=RlNtE85-k-g

see at 02:50

he problem of usabilityLondon Millenium Bridge

after 01:15

https://www.youtube.com/watch?v=7GuRPlWnrto

statics 2017: lecture 1

Summary of previous semester

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

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)

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

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

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)

3-hinged structure >> coping with horizontal support reactions of roofs

timber slab + roof:no problem

tie beam

!

modern buildings with functional use of roof:tie beam not possible

timber slab + roof:no problem

tie beam

!

!

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

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

statical determinacy: classification of structures

structures

determinate

indeterminate overdeterminate

indeterminate and overdeterminate

statical determinacy: classification of structures

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

határozatlan túlhatározott

határozatlan és túlhatározott

határozotte=i

detM ≠0

e=idetM = 0

e < i e > i

statical determinacy: examples

Complex structures >> smart way of finding

support reactions

Next week: