CONCEPTE / TEOREME MATEMATICE DE UZ PRACTIC

BETON SI STRUCTURI DIN BETON 1.

Indicate working stages for: ultimate limit state, deflection and cracking control

Cerinţe: indicarea stadiilor III si II Punctaj comparativ intre subiecte: 5 Answer: Working stage III is used for ultimate limit state, deflection & cracking control is based on stage II.

2.

Reinforced concrete element durability: concrete cover

Cerinţe: desen care sa reflecte stratul de acoperire; se va preciza rolul stratului de acoperire Punctaj comparativ intre subiecte: 10 Answer: Minimum concrete cover shall be provided for a safe transmission of bond forces, protection of steel against rust, appropriate fire resistance.

3.

Limit state method: design characteristics of concrete and reinforcement

Cerinţe: se vor indica rezistentele caracteristice si de calcul; se vor desena curbele - Punctaj comparativ intre subiecte: 8 Answer: Concrete: characteristic compressive strength: ; average tensile strength characteristic tensile strengths and ; design strengths are

;

Reinforcement: characteristic strength fyk is natural yielding limit (Re - limit of elasticity) or 0.2 proof test R0.2; design strength:

Simplified diagram Design diagram

4.

Indicate limit states for reinforced and prestressed concrete elements

Cerinţe: se vor enumera toate starile limita Punctaj comparativ intre subiecte: 6 Answer: ultimate limit states (exhausting of bearing resistence; loss of static equilibrium & fatigue); serviceability limit states (cracking; deformations; stress control)

5.

Available strain diagram in bending with axial force (3 pivots rule)

Cerinţe: se va intocmi schita care prezinta cei 3 pivoti

Punctaj comparativ intre subiecte: 10

compression tension

Answer:

6.

Simple reinforced rectangular section in bending

Cerinţe: desen reprezentand sectiunea, diagrama deformatiilor specifice si a eforturilor unitare; ecuatiile de echilibru Punctaj comparativ intre subiecte: 10 Answer: cu fcd Fc 0,8x x h

G

d

z = d - 0,4x

MEd d1 -

As1

s1

Fs1 = As1fyd

equilibrium in longitudinal direction:

Fc  Fs1  0 0,8bxf cd  A s1f yd  0

-

7.

moment equilibrium: M Ed  Fc z  0 ; M Ed  0,8bxf cd d  0,4x   0 M Ed  Fs1z  0 ; M Ed  A s1f yd d  0,4x   0

Definition of three shear forces involved in calculation to shear

Cerinţe: se vor scrie simbolurile pentru cele trei forte si se va explica ce reprezinta fiecare dintre ele Punctaj comparativ intre subiecte: 8 Answer: Vrd,c – design shear resistence of element without shear reinforcement; Vrd,s – design value of shear force which can be sustained by yielding of shear reinforcement; Vrd,max – design value of maximum shear force which can be sustained by crushing of concrete

8.

Concept of prestressing

Cerinţe: se vor desena diagramele de eforturi unitare produse de efortul de precomprimare, incarcari, precum si cumularea acestora; se va explica ce reprezinta fiecare diagrama; se va face o comparative Punctaj comparativ intre subiecte:10 Answer: Reinforced concrete section is cracked under service loads; reduced stiffness; risk of reinforcement corrosion Prestressed concrete section is fully in compression and stiffer section; reduced risk of reinforcement corrosion

T

+ Ap

C prestressing

= T loads

C

9.

Prestressing technologies

Cerinţe: se vor intocmi schite care reflecta cele doua modalitati de realizare a precomprimarii si se vor descrie etapele principale de lucru Punctaj comparativ intre subiecte: 8 Answer: Pretensioning – tendon is subjected to tension before casting of concrete Required steps: tendon tensioning; casting of concrete; heat curing; transfer = releasing of tendon at  70% compressive strength of concrete. tendon

abutment

long line of prestressing

Post-tensioning – tendon is subjected to tension after casting & curing of concrete Required steps: element provided with a duct; tendon introduction in the duct; transfer = tensioning of the tendon; tendon anchorage; filling the duct with grout. tendon duct

jack

grout

10.

anchorage

Prestressed concrete: decompression state of the section

Cerinţe: desen reprezentand starea de decompresiune value of prestressing force and bending moment Punctaj comparativ intre subiecte: 7 Answer: Decompression = section fully in compression and zero stress at bottom side under action of prestressing force after all losses and bending moment induced by loads (usually in frequent combination)

MEf C

Ap

P

11. Which are the particularities of the slabs with main reinforcement in two directions (short span)? Requirements: indication of the correlation between the bending moment ratio my/mx and of the span ratio ly/lx Answer: The necessity of reinforcement of the short span is obtained from Figure where M Y/Mx and ly/ lx it is given. For the case when 0.5< ly/ lx