Chapter 4 - Flexure King Saud University University Civil Engineering Department Reinforced Concrete Design Prof. Dr. Mohammad Jamal Al-Shannag

Flexural Stress There are three types of flexural failure of a structural member. Steel may reach its yield strength before the concrete reaches its maximum. (Under-reinforced section). Steel reaches yield at same time as concrete reaches ultimate strength. (Balanced section). Concrete may fail before the the yield of steel due to the presence of a high percentage of steel in the section. (Over-reinforced section).

Flexural Stress Steel may reach its yield strength before the concrete reaches its maximum. (Under-reinforced section).

Flexural Stress Steel reaches yield at same time as concrete reaches ultimate strength. (Balanced section).

Flexural Stress Concrete may fail before the the yield of steel due to the presence of a high percentage of steel in the section. (Over-reinforced section).

Basic Assumptions in Flexure theory of RC Members (Strength Design Method) 1.plane section before bending remain plane after bending 2.the strain in reinforcements equals to the strain in concrete at the same level (no slip). 1 & 2 imply that strain in reinforcement and concrete is directly proportional to the distance from N.A. 3.the tensile strength of concrete is neglected in flexural strength calculations. 4. the stresses in concrete and reinforcement are calculated from strains using material stress-strain curves. Exception. For steel

5. concrete is assumed to fail when compressive strain at the extreme compression fiber reaches 6. The compressive stress block for concrete may be replaced by an equivalent stress block of rectangular, trapezoidal, parabolic or any other shape provided that the predicted strength results are in substantial agreement with comprehensive test results. Fig. 2 shows an equivalent rectangular stress block adopted by SBC-304 (Sec ). In the figure  1 shall not be smaller than 0.65 See SBC-304, Section 10.2 and MacGregor chapter 4.

R For design, the SBC 304 allows the use of an equivalent rectangular compressive stress distribution (stress block) to replace the more exact concrete stress distribution. In the equivalent rectangular stress block, an average stress of 0.85 fc‘ is used with a rectangle of depth a=β 1 c β1= 0.85 for concrete with fc‘ = 30 MPa and 0.05 less for each 7 MPa of fc‘ in excess of 30 was determined experimentally. Research data from tests with high strength concretes10.1,10.2 supported the equivalent rectangular stress block for concrete strengths exceeding 55 MPa, with a β1= The equivalent rectangular stress distribution does not represent the actual stress distribution in the compression zone at ultimate, but does provide essentially the same results as those obtained in tests.10. 3

Fig. R Strain distribution and net tensile strain.

New Definitions of failure modes, and strength reduction factors (SBC 304). Fig. R Variation of ø with net tensile ɛ t and c/d t for Grade 420 reinforcement and for prestressing steel.