1. Shear Forces and Bending Moments in Beams
Chapter 13 Strengths

2. 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

3. Types of Beams Types of Beam Support Types of Beams Roller Support
Hinge Supports
Fixed Supports
Types of Beams
Simple Beam
Overhanging Beam
Cantilever Beam
Propped Cantilever Beam
Fixed Beam
Continuous beam

4. 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

5. Beam Reactions Review Beam Reaction calculations Example 13-1

6. 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.

7. 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.

8. 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.

9. 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.