6 Flexural StressThe compressive zone is modeled with a equivalent stress block.
7 Flexural StressThe equivalent rectangular concrete stress distribution has what is known as a b1 coefficient is proportion of average stress distribution covers.
8 Flexural Stress Requirements for analysis of reinforced concrete beams  Stress-Strain Compatibility – Stress at a point in member must correspond to strain at a point. Equilibrium – Internal forces balances with external forces
9 Flexural Stress Example of rectangular reinforced concrete beam. (1) Setup equilibrium.
13 Strain Limit Method for Analysis and Design If the net tensile strain in the extreme tension fibers, et is small, being equal or less than a compression-controlled strain limit, a brittlemode of failure is expectedFor the tension-controlled state, the strain limit et = corresponds to reinforcementRatio = 0.63, where is the balanced reinforcement ratio for the balanced strain et =0.002 in the extreme tensile reinforcement.
15 Mode of failure Compression Failure The concrete will crush before the steel yields. This is a sudden failure.The beam is known as an over-reinforced beam.
16 Tension FailureThe reinforcement yields before the concrete crushes. The concrete crushes is a secondary compression failure.The beam is known as an under-reinforced beam.
17 Balanced FailureThe concrete crushes and the steel yields simultaneously.The beam is known as an balanced-reinforced beam.
18 Critical thinkingIn order to prevent such a state of behavior in flexural members, a strain greater than in the extreme tensile reinforcement has to be required in design.For example, if 60 grade steel (410 Mpa) is used as reinforcement, the yield strainThe design has to be based on (termed at the level of the extreme tensile reinforcement layer) sufficiently larger than in flexural members to ensure ductile performance.
19 Notes =balanced neutral axis depth at limit strain =effective depth to the extreme tensile reinforcement layer