Calculation of flexible elements with double reinforcement

Sections with double reinforcement are those in which, in addition to tensile reinforcement, is placed, compressed by calculation. The need for compressed reinforcement arises when a section with a single reinforcement cannot perceive the design moment from an external load, due to the insufficient strength of the concrete of the compressed zone (destruction in case II, when ). In order for the compressed zone in such constructions to absorb all the compressive forces, it must be reinforced with reinforcement. Sections with double reinforcement are not economical in terms of steel consumption, since increased consumption of longitudinal reinforcement. Therefore, compressed reinforcement is installed by calculation only in special cases: with limited dimensions of the cross section of the element and the impossibility of raising the concrete class is impossible.

Formulas for calculating normal sections with double reinforcement will be obtained, as well as the section with one reinforcement, having designed all the forces on the element axis and having made the equation of moments relative to the center of gravity of the tensioned reinforcement

(12)

The first term of the resulting equation is the moment perceived by the section with a single reinforcement, which, when using tabular data, can be expressed by the formula

Therefore, the formula will take the form

(3)

When calculating cross sections of elements with double reinforcement, two types of problems can occur:

1. compressed reinforcement is necessary to strengthen the compressed zone of concrete (if an increase in cross-sectional dimensions is undesirable)

2. compressed reinforcement is provided for structural considerations.

When solving problems of the first type, in the two initial equations (1) and (3) there appear three unknowns x, As, A's

Studies have shown that the cross section will be most economical when the maximum possible compressive force is transferred to the concrete. This will be the case if Consequently, additional conditions are accepted that meet economic requirements.

In this case, the compressed reinforcement will perceive the moment:

(four)

From here we find the cross-sectional area of ​​compressed reinforcement

(five)

The area of ​​tensile reinforcement AS will be obtained from condition (1), taking

(6)

Task

Given: Rb = 8.5 0.85 = 7.23 MPa

b = 25 cm Rs = 280 MPa

h = 50 cm Rsc = 280 MPa

M = 220 kNm = 0.62

B15; = 0.85 A0max = 0.43

A II h0 = ha = 50-4 = 46 cm

a = 4 cm Find A0, as for a section with a single reinforcement

a / = 3 cm

As-? As / -?

Because This means that a section with a single reinforcement cannot fully perceive the acting moment, then it is necessary to deliver the calculated compressed reinforcement, having determined its area by the formula (5)

According to the formula 6 we calculate:

Take compressed reinforcement 2 18 AII with As / fact = 5.09cm2

Accepted tensile reinforcement 4 28 AII with Asfact = 24.63 cm2

Reinforcement

1. 9000-20 = 8980

2. 8980-30 = 8950

3. 8950/4 = 2237

4. 2237/160 = 13

5. 160 13 = 2080

6. 2080 2 = 4160

7. 8950-4160 = 4790

8. 4790/370 = 12

9. 370 12 = 4440

10. 4790-4440 = 350

11. 350/2 = 175 = 160 + 15