Chapter 4 - Flexure. Lecture Goals Structures Basic Concepts Rectangular Beams.

Chapter 4 - FlexureChapter 4 - Flexure

Lecture GoalsLecture Goals

StructuresBasic ConceptsRectangular Beams

Rectangular Beams:- Simply Supported

Continuous Beams

Flexural StressFlexural Stress

The beam is a structural member used to support the internal moments and shears. It would be called a beam-column if a compressive force existed.

C = T

M = C*(jd)

= T*(jd)


The stress in the block is defined as:

M*y) / I

Sxx = I / (ymax)

The equation for Sxx modulus for calculating maximum compressive stress.

Sign Convention: +M, -M

Basic Safety Equation for Flexure:

Art. 9.1.1 (SBC 304) design strength required Strength design strength=nominal strength, e.g. Mn, Vn, ….

required strength=load effect resulting from factored loads, Mu, Vu, ….

For Beam design, the design criteria become

Mn Mu and Vn Vu

Mu= factored load moment, (Moment computed from combination of factored loads)

Vu= factored load shear, (Shear computed from combination of factored loads)

: Strength reduction factor to account for variations in dimensions, and material strengths.


The three main stages of the beam.

Stage 1: No external loads acting on the beam.

Stage 2: Service loading on the beam.

Stage 3: Beam failure.


The moment-curvature diagram show the five stages of the beam. The plot is of the curvature angle, , verse the moment.

= ( / y) = [ / E ] / y

= [(My / I) / E] / y

= M / ( E I )


The beam fails first in shear and the second beam fails in bending moment.


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).


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).

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).

Chapter 4 - Flexure. Lecture Goals Structures Basic Concepts Rectangular Beams.

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Transcript of Chapter 4 - Flexure. Lecture Goals Structures Basic Concepts Rectangular Beams.