Cours Calculation civil engineering EN.pptx

Calculation for a civil engineering

1. Example of calculations for a civil engineering project Project presentation Calculation and application of loads Physical model (boundary & initial conditions) Internal forces calculation (M,N,V) Dimensioning and checking (Calculation assumptions, Stresses and Strain )

2. Vertical gravity loads Actions with a horizontal or vertical ascending c omponent NATURE OF THE MECHANICAL ACTIONS ACTING ON STRUCTURES Calculation and loads application

3. Dead load (self weight of structures or overloading materials ) Loads related to the operation of buildings (public, furniture , stocking , maintenance overloads ) Climatic snow loads Q Sn eurocode VERTICAL GRAVITY LOADS dead load (G) live load (Q) snow (Sn) Simplified model G Calculation and loads application

4. Earthquake : masses accelerations resulting in horizontal forces Vibrations of rotating machines Eurocode Acceleration (A n ) Vibrations ( w ) Earth pressure, liquids or ensiled materials Pressures or depressions due to the wind Wind pressure (W) Earth pressure Horizontal pressure ( ρ h) Wind pressure (W) Vibrations of rotating machines w Calculation and loads application Wind Swirling flow area Regular flow area

5. ROOFING 2- the structural frame carries the roofing and the ceiling . STRUCTURAL FRAME CEILING 3- The walls support the previous vertical loads. WALL 4- The floor , in addition to his self weight , carries operating expenses (fourniture, people etc..). FLOOR 5- The foundation walls in turn transmit the loads to the foundations. 6- Foundations distribute the pressures of BASEMENT on the soil and ensure the static equilibrium of the construction. FOOTPLATES FOUNDATION SUB-GRADE Example of vertical loads calculation on load-bearing elements 1- The roofing undergoes climate action (snow). SNOW Actions ascending from the load-bearing ground Physical model (boundary & initial conditions) Calculation and loads application

6. Example of actions with a horizontal component on the load-bearing elements of a two- storey building Wind forces applied at nodes Wind depression Turbulences Leeward side Ground floor First floor Second floor Wind pressure Wind Windward side Wind forces applied at nodes Calculation and loads application Acceleration (A n )

7. Example of actions with an horizontal or ascending vertical component on the load-bearing elements Hydrostatic thrusts Active earth pressure Active earth pressure Leeward side Basement Ground floor Wind pressure Wind Windward side Wind depression Turbulences Calculation and loads application

8. The Calculation of vertical loads on a structure The Calculation of vertical loads on a structure makes it possible to know, level by level, element by element, the path or distribution of external mechanical actions throughout the whole construction, starting from the highest point of the building, towards the foundations and the ground. The structure as a whole, as well as its components, must be designed to be stable and resistant to these actions. The Calculation of vertical loads on a structure is the basis for the dimensioning of the load-bearing structures and in particular the foundations. Ascending loads from the load-bearing ground Calculation and loads application

9. Physical model ( Boundary & initial conditions) Y Only one connection unknown : Y Ascending loads from the load-bearing ground

10. Two unknowns of connection : X and Y Y X Ascending loads from the load-bearing ground Physical model ( Boundary & initial conditions)

11. Y X M Three unknowns of connection : X , Y and M Ascending loads from the load-bearing ground Physical model ( Boundary & initial conditions)

12. Effort calculation (M,N,V) for each element Where ?? Global and local coordinate systems G How ? Simplified physical model BASIC PRINCIPLE OF STATICS - (B.P.S) NOTA : The BPS is the only way to solve isostatic systems . If the systems are hyperstatic , other equations must be found with more in-depth calculation methods. ( energy method, force method, Clapeyron equation …) Ascending loads from the load-bearing ground Global coordinate system Local coordinate system Cut-off Cutting plan Cross-section S(x) Left -hand Section Right-hand section

13. This is the field of strength of materials or mechanics of materials ( MoM ) . Material assumptions : Continuity  : The material does not show any structural discontinuity within the parts under consideration. Homogeneity  : The physico -chemical composition remains unchanged regardless of the elementary volume considered within the material. Isotropie: The mechanical properties are the same in all directions. Geometric assumptions : In MoM , the neutral axis displacements are small compared to the dimensions of the beam . The loads are calculated in the initial configuration. Navier and Bernoulli : C ross-sections remain plane and perpendicular to the deformed neutral axis in the deformation of the beam. Saint-Venant : If we know the loads (N, V and M) on the left side of a sections , we can determine its constraints. . Dimensioning and checks ( Calculation assumptions , Stresses and strains )

14. p u B A F x y F 4,700 900 900 Vy(x) (kN) x -4,458 4,458 -6,392 6,392 -8 -6 -4 -2 8 6 4 2 Mz(x) (kN.m) x 4,605 -2,906 -2,906 -8 -6 -4 -2 8 6 4 2 The distribution of effort in each element . Effort calculation (M,N,V) for each element Ascending loads from the load-bearing ground

15.   Shearing Stress and strain SHEARING The stress on the cross-section is z y x τ y G In the plan x z y x Vy (x) The shear displacement is Dimensioning and checks ( Calculation assumptions , Stresses and strains )   Ascending loads from the load-bearing ground

16. SIMPLE COMPRESSION if N<0 SIMPLE TENSILE if N>0 The stress on the cross-section is x N(x) z y x G z y x σ G y In the space σ y G In the plan The strain on the cross-section is Attention to instabilities , buckling risk ! Dimensioning and checks ( Calculation assumptions , Stresses and strains ) Ascending loads from the load-bearing ground

17. DIFFERENT STATEMENTS OF LOADS SIMPLE BENDING The stress on the cross-section is The strain on the cross-section is The camber of the cross-section is Mz(x) x z y x Vy(x) z y x σ G y σ y G In the space In the plan Ascending loads from the load-bearing ground

18. Stress and strain COMOUND BENDING Mz(x) x z y x Vy(x) N(x) σ y G z y x σ G y Ascending loads from the load-bearing ground Dimensioning and checks ( Calculation assumptions , Stresses and strains ) In the space In the plan The stress on the cross-section is The strain on the cross-section is

19. BI-AXIAL BENDING G Mz(x) x z y x Vy(x) Vz(x) My(x) z y x σ G y Ascending loads from the load-bearing ground Dimensioning and checks ( Calculation assumptions , Stresses and strains ) The stress on the cross-section is The strain on the cross-section is The camber of the cross-section is In the space

20. For elements dimensioning, it suffices to check that □ The stresses calculated with the loads remain less than or equal to those which the element can resist . σ cal ≤ σ adm □ D isplacements calculated with the loads remain less than or equal to those given in building codes . fcal ≤ fadm Dimensioning and checks ( Calculation assumptions , Stresses and strains )