Basic Design Principles For Reinforced Concrete Beam Dr. M.E. Haque, PE

A Simply Supported Reinforced Concrete Beam - N.A. P = 0 A A - A Dr. M.E. Haque, PE

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

Typical Stress-Strain Curves for Concrete and Reinforcing Steel Dr. M.E. Haque, PE

1. Un-cracked Concrete stage N.A.(Zero Stress Line) P Compression Tension R (Radius of Curvature) Dr. M.E. Haque, PE

1. Un-cracked Concrete stage P Compression Tension 1. Un-cracked Concrete stage Dr. M.E. Haque, PE

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

At ft = fr , where modulus of rupture, fr = 7.5 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) C=0.5fc x (b x0.5h) T=0.5ft x (b x0.5h) 2/3 h b 1/2 h ft fc Stress diagram M Section 1-1 fc = ft = Mc/Ig where c = 0.5h Ig = bh3/12 OR 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 Dr. M.E. Haque, PE

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

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

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

C c T Concrete in compression 1 fc b M Reinforcing Steel in tension Neglect concrete in tension Concrete in compression Reinforcing Steel in tension Dr. M.E. Haque, PE

Dr. M.E. Haque, PE