Shear Forces and Bending Moments in BeamsChapter 13 Strengths

Introduction• Beams are members that carry transverse loads and are

subjected to bending• Any member subject to bending is referred to as a beam• Beams considered in this course are limited• Straight and uniform cross section• Horizontal• Subject to forces applied in vertical plane

Types of Beams• Types of Beam Support• Roller Support• Hinge Supports• Fixed Supports

• Types of Beams• Simple Beam• Overhanging Beam• Cantilever Beam• Propped Cantilever Beam• Fixed Beam• Continuous beam

Types of Loading• Concentrated Loads – applied at a specific point • Uniform Loads – distributed over a part or the entire length• Linearly Varying Loads –distributed load with uniform

variation of intensity

Beam Reactions• Review Beam Reaction calculations• Example 13-1• Example 13-2

Shear Force and Bending Moment in Beams• Internal shear force and bending moment are developed in a

beam to resist the external forces and to maintain equilibrium• Finding internal forces at section, pass a plane through the

section so the beam is separated into two parts• The entire beam is in equilibrium each part of the beam

separated must also be in equilibrium• Beam Sign conventions – Internal shear forces• Positive shear – cause beam to move up on the left side• Positive moment – external forces produce a bending effect to

bend concave upward.

Internal Shear Force and Bending Moment Rules• For Finding Shear Forces – the internal shear force at any

section of a beam is equal to the algebraic sum of the external forces on either segment separated by the section. If the summation is from the left end of the beam to the section, treat the upward forces as positive. If the summation is from the right end of the beam to the section, treat the downward forces as positive.

• For Finding Bending Moments – the internal bending moment at any section of a beam is equal to the algebraic sum of the moments about the section due to the external forces n either segment separated by the section. In either case treat the moment produced by upward forces as positive.

Shear Force and Bending Moment Diagrams• Shear force and bending moment diagram show shear force

and bending moment along the beam• Diagrams show magnitudes and locations of the maximum

shear force and the maximum bending moment.

Relationship load, Shear, Moment• Slope of the shear diagram at any section is equal to the load

intensity at that section• Shear force at a section is equal to the shear force at the

previous section plus the total load between the two sections. • Shear diagram has an abrupt change at the concentrated load,

an upward force will cause an abrupt increase in the shear force, downward force will cause an abrupt decrease in the shear force.

• Slope of the moment diagram at any section is equal to the value of the shear force at that section

• The moment at a section is equal to the moment at the previous section plus the area under the shear diagram between the two sections.