BASIC ASSUMPTIONS IN FLEXURE

THEORY 1. Plane sections before bending remain plane after bending.

2. Strain in concrete is the same as in reinforcing bars at the same level, provided that the bond between the steel and concrete is sufficient to keep them acting together under the different load stages i.e., no slip can occur between the two materials.

3. The stress-strain curves for the steel and concrete are known.

4. The tensile strength of concrete may be neglected.

5. At ultimate strength, the maximum strain assumed equal to 0.003, by the Egyptian Code.

The assumption of plane sections remaining plane

Note we see .0035&.00107 in other

codes

Noncracked, Linear Stage

moments are small, compressive stresses are very low and the maximum tensile stress of concrete is less than strength, fctr.

Cracked, Linear Stage

When the moment is increased beyond Mcr, The stress-

strain curve for concrete is approximately linear up to

0.40 fcuconcrete in compression has not crushed. , the

elastic (straight line) theory formula M/Z may be used

to analyze

Cracked, Nonlinear Stage

For moments greater than these producing stage 2, the

maximum compressive stress in concrete exceeds 0.40.

However, concrete in compression has not crushed the

flexural formula M/Z of the conventional elastic theory

cannot be used

Ultimate Strength Stage

nominal Strength

Nominal without f.o.s

TYPES OF FLEXURAL FAILURE

-TEN

the steel will reach its yield strength before the

concrete reaches its maximum capacity.

the strain in the extreme compression

approximately 0.003,

The section then fails in a "ductile" fashion with

adequate visible warning before failure.

Balanced Failure

At a particular steel content, the steel

reaches the yield strength and the

concrete reaches strain of 0.003

Compression Failure

the concrete may reach its maximum capacity

before the steel yields. The section then fails

suddenly in a "brittle" fashion if the concrete is

not confined and there may be little visible

warning of failure.

Minimum Effective Depth with

Maximum Steel

example