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# Basic Design Principles For Reinforced Concrete Beam

Basic Design Principles For Reinforced Concrete Beam. P = 0. A. N.A. A - A. A. A Simply Supported Reinforced Concrete Beam -. R (Radius of Curvature). Compression. P. N.A.(Zero Stress Line). Tension. Three stages before collapse: 1. Un-cracked Concrete stage

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## Basic Design Principles For Reinforced Concrete Beam

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1. Basic Design Principles For Reinforced Concrete Beam

2. P = 0 A N.A. A - A A A Simply Supported Reinforced Concrete Beam -

3. R (Radius of Curvature) Compression P N.A.(Zero Stress Line) Tension Three stages before collapse: 1. Un-cracked Concrete stage 2. Cracked Concrete (tension zone) - Elastic Stage 3. Cracked Concrete (tension zone) - Ultimate Strength Stage

4. R (Radius of Curvature) Compression P N.A.(Zero Stress Line) Tension 1. Un-cracked Concrete stage

5. Compression P Tension 1. Un-cracked Concrete stage

6. Compression zone d h Stress Diagram Strain Diagram b Compressive Stress fc' Tension Zone ft = fr = 7.5 fc' Tensile Stress 1. Un-cracked Concrete Stage ft < fr M < Mcr fc = ft << fc' fc ft = fc Stress-Strain Diagram for Concrete

7. Section 1-1 fc C=T ; fc = ft M = 0.5fc x (b x 0.5h) x (2/3 h) = 1/6 fc x b x h2 fc = ft = 6M/(bh2) fc = ft = Mc/Ig where c = 0.5h Ig = bh3/12 C=0.5fc x (b x0.5h) OR 1/2 h M At ft = fr , where modulus of rupture, fr = 7.5 fc’ Cracking Moment Capacity, Mcr = fr x Ig/(0.5h) = (fr x b x h2)/6 2/3 h 1/2 h T=0.5ft x (b x0.5h) ft b Stress diagram

8. Compression zone c < 0.003 d h fs =0.5 fy s = fs/Es Stress Diagram Strain Diagram b Compressive Stress Tension Zone Concrete Cracked fc' 0.45fc' fy  0.003 0.5fy ft = fr = 7.5 fc' Es Tensile Stress  Stress- Strain Diagram for Reinforcing steel in Tension Stress- Strain Diagram for Concrete in Compression 2. Cracked Concrete (Tension Zone) - Elastic Stage ft > fr M > Mcr fc = 0.45fc' fs =0.5 fy

9. Compression zone c = 0.003 d h T = Asfy s = fy/Es Stress Diagram Strain Diagram b Compressive Stress Tension Zone Concrete Cracked fc' fy Es 0.003  Stress-Strain Diagram for Concrete in Compression Stress-Strain Diagram for Reinforcing Steel in Tension 3. Cracked Concrete (Tension Zone) - Ultimate Strength Stage ft > >fr M > >Mcr fs = fy fc = entire stress block until compression failure 

10. COMPRESSION TENSION Figure 4 Manipulated Image visualization for flexural failure. (Digital image from Northridge Collection, Earthquake Engineering Research Center, University of California, Berkeley)

11. Concrete in compression 1 fc C b M c T Reinforcing Steel in tension 1 Neglect concrete in tension

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