COLLECTION OF LOADS ON THE BEAM.

To collect the load on the beam, you need to cut from it 1pm and load ) multiply by distance beams, and then calculate the bending moment.

When calculating bending rectangular elements with a single reinforcement, there are 3 types of tasks:

Type 1

Given

The dimensions of the section b * h (see), a, M, Yвi, the class of concrete and the class of reinforcement. It is required to determine As and construct the section.

Decision:

1. According to Vol. 2.3 [Ts.] P. 63 we define Rb (MPa)

2. According to V. 2.8 [C.] p. 73 we define Rs (MPa)

3. Determine the working height of the section ho = h

4. Calculate Ao; Ao = M / Rb ho2 b

5. According to t. 3.2 [C.] p.90, taking into account the class of concrete, steel, we find Aomax

6. Comparing the values ​​of Ao and Ao max, if Ao £ Ao max, then we have a single reinforcement.

7. According to the found value of Ao by m. 3.1 [C.], we find .

8. Determine the required cross-sectional area of ​​reinforcement As: As = M / Rs ho

9. According to Appendix 2 [C.] p.431, we take the required number of rods and ¯ reinforcement, taking into account that the accepted area of ​​reinforcement must be equal to, or somewhat larger than, the area of ​​reinforcement obtained by calculation.

10. Construct a section.

Type I task .

Given:

Sizes of section b * h = 20 * 40 (see),

a = Zsm.

M = 110 kNm

Concrete class B20; Yi = 0.9

steel grade A II.

Determine the required amount of reinforcement and to construct the section.

Decision:

Rb = 11.5 0.9 = 10.35 mPa,

Rs = 280mPa,

ho = ha = 40-3 = 37 cm

Ao = 110 • 105 / 10.35•20•372 (100) = 0.0388 <Ao max = 0.43

Ao = 0.0388 => = 0.995

As = 110 • 105 / 0.995 • 280 • 37 (100) = 14.4 cm2.

Accept 3 ¯ 25 A II with Asfact = 14.43 cm2.

Type 2

Given:

The dimensions of the cross section b * h, the value of a, the coefficient of the working condition Ybi

Bending moment M, class of concrete and reinforcement, area of ​​tensile reinforcement As.

Determine M £ Msech?

Decision:

1. According to the table. 13 SniP 2.03.01-84 or m. 2.3 [C.] we find the value of Rb (mPa)

2. According to the table. 2.8 [C.] => Rs.

3. Determine the working height of the section ho = h - a

4. Determine the height of the compressed zone section: x = RsAs / Rbb

5. Determine the relative height of the compressed zone of concrete. = x / h0.

6. According to table. 3.2 [C.] p.90, taking into account the class of concrete and reinforcement, we find the value of the boundary height of the compressed zone of concrete | R.

7. If £ y, then check the strength of the section from the condition:

M £ RsAs (ho - 0,5x)

8. We conclude about the bearing capacity of the element. (This calculation is typical for major repairs)

Problem number 2

Given:

Dimensions sech. b * h = 30 * 60 (see); a = 3 (see); Yi = 0.9; M = 160 kNm;

concrete class B40. reinforcement class A II, reinforcement quantity 4 ¯ 22

with As fact. = 15.2 cm2.

Check: M £ Msech

Decision:

Rb = 22 * ​​0.9 = 19.8 MPa; Rs = 280 MPa;

ho = h - a = 60 - 3 = 57 cm.

x = RsAs / Rbb = 280 * 15.2 / 19.8 * 30 = 7.16 cm.

y = 0.52 according to t. 3.2. [P] p.90

= x / ho = 7.16 / 57.5 = 0.1245 < y = 0.52 => single reinforcement.

Msech = RsAs (ho - 0.5x) = 280 * 15.2 * (57.5 - 0.5 * 7.16) * (100) = 22948000 Ncm = 229.48 kNm

M = 160 <MSt = 229.48 kNm - the cross section strength is ensured.

Problem number 3

Given:

Dimensions sech. b * h = 32 * 68 (cm), a = 3.8 cm, B20; Yi = 0.9; M = 205 kNm; reinforcement class A III, As = 10.05 cm2. Identify: M £ Msech

Decision:

Rb = 11.5 * 0.9 = 10.35 MPa, Rs = 365 MPa,

ho = ha = 68-3.8 = 64.2 cm.

x = Rs * As / Rb * b = 365 * 10.05 / 10.35 * 32 = 11.075 cm. = x / ho = 11.075 / 64.2 = 0.173 <| y = 0.59 => single reinforcement.

Msech = RsAs (ho - 0.5x) = 365 (100) 10.05 (64.2 - 0.5 * 11.075) = 21518000 Ncm 215 kNm.

M = 215> Msec = 205 KN m - cross section strength is not ensured, it is necessary to reinforce additionally => by = 0.173 => = 0.9052

As = 215 * 105 / 0.9052 * 365 * 64.2 * (100) = 10.4 cm2. We take 3 22 22 A III with As = 11.4 cm2.

T ipa 3

Task number 4

This type of tasks is adopted in the calculation of new designs, or reconstruction, in the case of replacement of elements.

Given:

B 30, Yvi = 0.9; M = 90kNm, a = 3.2 cm., Rebar class AIII;

Define: As; b; h.

Decision:

1. By tab. 2.3 => Rb = Rb * Yi = 17 * 0.9 = 15.3 MPa.

2. According to tab. 2.8 => Rs = 365 mPa.

3. Accept = 0.25 (for beams 0.2 ... 0.4)

(for plates = 0.1 ... 0.15)

4. Accept b = 20 ... 40 cm

5. According to the table. 3.1 => A0 = 0.219 = 0.25

6. Find ho = M / A 0 * Rb * b =

7. We define h = h0 + a = 36.65 + 3.2 = 39.85 cm round up to 40 cm.

8. Specify ho = h = 40-3.2 = 36.8 cm.

9. Determine the actual Ao:

Ao = M / b ho2 Rb = 90,105 / 20 * 36.82 15.3 = 0.212

10. According to Table. 3.2 find Ao max = 0,39

Ao = 0,217 <Ao max = 0,39 => = 0.8775

As = M / Rs ho = 90 105 /0.8875*365*36,8* (100) = 7.64 cm2.

Accept 3 ¯ 20 AIII with Asfact = 9.41 cm2.

Calculation of flexible elements of rectangular cross section. (type 1)

Find A s

Calculation of flexible elements of rectangular cross section.

Check M <Msech Type 2

Questions for self-test.

1. Estimated concrete compressive strength.

2. Estimated resistance of reinforcement tensile.

3. Standard concrete resistance to stretching.

4. Estimated resistance of concrete to stretching.

5. in-

6. h-

7. h0 =

8. a

9. As

10. Avs

11. x =

12. Zb =

13. =

14. y =

15. m

16. Formula 3

17. Formula 4

18. Ns =

19. Nb =

20. What is the basis for the calculation of the 1st, 2nd, 3rd stages of work of the bent elements?

Questions for self-monitoring on the topic:

"Flexable reinforced concrete elements of rectangular section".

1. Types of reinforcement according to the nature of work in bending elements.

2. Types of reinforcement by type of surface in bending elements.

3. Principles of reinforcement of bent elements of rectangular cross-section.

4. What is the percentage of reinforcement bent elements?

5. What is the minimum percentage of reinforcement of bent elements?

6. At what stage are bent reinforced concrete elements of rectangular cross section calculated?

7. What is: c , h, h0 = ha, as, abc, x, z?

8. What is equal to the distance a?

9. What are the cases of exhaustion of bearing capacity of bent elements?

10. Boundary condition between the 1st and 2nd cases of calculation?

11. What are the internal forces equal in the limit state?

12. What static conditions are used in the calculation of bent elements?

13. Formulas for the calculation of bending reinforced concrete elements of rectangular cross section: A0, As ,?

14. What are the three types of problems of calculating bent reinforced concrete elements of rectangular section?

15. How is the diameter and spacing of transverse reinforcement in a bent reinforced concrete elements of rectangular cross section?

16. Types of reinforcement according to the nature of work in bending elements.

17. Types of reinforcement by type of surface in bent elements.

18. Principles of reinforcement of bent elements of rectangular cross-section.

19. What is the percentage of reinforcement of bent elements?

20. What is the minimum percentage of reinforcement of bent elements?

21. At what stage are bent reinforced concrete elements of rectangular cross section calculated?

22. What is: c , h, h0 = ha, as, abc, x, z?

23. What is equal to the distance a?

24. What are the cases of exhaustion of bearing capacity of bent elements?

25. The boundary condition between the 1st and 2nd cases of calculation?

26. What are internal forces equal in the limit state?

27. What are the static conditions used in the calculation of bent elements?

28. Formulas for the calculation of bending reinforced concrete elements of rectangular section: A0, As ,?

29. What are the three types of problems of calculating bent reinforced concrete elements of rectangular section?

30. How is the diameter and spacing of transverse reinforcement in a bent reinforced concrete elements of rectangular cross section?

Technical dictation number 1

1. Limit - this is the condition of the building structure -

2. Calculation for the first group of limit states -

3. Calculation for the second group of limit states -

four. f -

five. P -

6 b and s -

7 bi and si -

8. Constant loads -

9. Temporary loads -

10. Short-term loads -

11. Special loads -

12. Regulatory loads -

13. Design load -

14. Rb

15. Rs

16. Rsp

17. RBP

18. Rb

19. Rbt

Technical dictation number 2

1. Estimated concrete compressive strength.

2. Estimated resistance of reinforcement tensile.

3. Standard concrete resistance to stretching.

4. Estimated resistance of concrete to stretching.

5. in-

6. h-

7. h0 =

8. a

9. As

10. Avs

11. x =

12. Zb =

13. =

14. y =

15. m

16. Formula 3

17. Formula 4

18. Ns =

19. Nb =