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REINFORCED AND PRESTRESSED CONCRETE I C7-

Reinforced and Prestressed ConcreteReinforced and Prestressed Concrete -- CC 77 --

Aqua, Chicago 2010

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The principal stresses and the cracks directions

- principal compression stresses

- principal tension stresses

(normal stresses)

(tangential stresses)

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2.1. The transversal reinforcements (stirrupsand bent-up bars) yield the widths of

inclined cracks increase, visibledeformations appear, and finally the

compressed concrete at the crack end iscrushed.

- Failures modes 2. inclined sections the bending moment + shear force action

2.2. The compressed concrete at the crack end

or in the beam core (T-beam) is crushedwithout the transversal reinforcements

yielding.

!only first type of failure is admissible

2.3. The transversal reinforcement lose the

adherence to concrete.

2.4. The longitudinal reinforcement lose theadherence to concrete.

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The influence of the reinforcements in the inclined sections

1. beams withouttransversereinforcements

2. beams withtransversereinforce-ments

steelyieldind

concretecrushing

reinforce-ments

pulling out

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The variation of tangential stress on the section height for double reinforced sections

simplyreinforced

section

doublereinforced

section

rectagular section

T section

simply reinforced

section

double reinforced

section

equivalent section

-the static moment of the tension reinforcement cancelthe static moment of the compressed concrete section.

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The variation of tangential stress on the section length

constant section height

linkedvariation

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The variation of tangential stress on the section length

variables

variable section height (haunche = vuta)

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dx

(z is a fraction of h0)

(+) if M and h0 increase in the same direction(-) if M and h0 increase in different directions

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1. Tooth-Comb model

- shear resistance of a beam withouttransverse reinforcements is:

EC2 :

Shear inconcrete

Vertical component ofthe granulosity effect

The shear component dueto the dowel (dorn) effect

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2. Arch with tie model (modelul arcului cu tirant)

simply supported beams

continuous beams

beam effect arch effect

If : => =>

If : => and

Zone between twoadiacent cracks

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3. Strut and tie model (modelul grinzii cu zabrele)

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Stirrups as shear reinforcement

Stirrups and the analogous truss

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Shear design flow chart.(stirrups as transversalreinforcement)1/2

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Shear design flow chart.(stirrups as transversalreinforcement)2/2

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Bent-up bars