REMINDERS HW#5 due Friday Feb 28 Read 4.5 for Friday 1

LESSON 14 STRENGTH OF MATERIALS SECTIONS 4.3 – 4.4

TODAY’S LESSON WILL COVER: Shear Forces and Bending Moments Relationships between Loads, Shears and Bending Moments 3

SHEAR FORCES AND BENDING MOMENTS When a beam is loaded by forces and/or couple moments, stresses and strains are created throughout the interior of the beam—we’ll investigate these in Chapter 5 To determine these stresses and strains, we must determine the internal forces and moments This is done by “slicing” the beam and exposing the normal, shear and bending moments—as we saw in statics—then using E of E to find the exposed forces and moment 4

SIGN CONVENTIONS—STATICS VS. DEFORMATION In statics, sign was based on direction: Up and right was positive Down and left was negative CCW moment was positive, CW moment was negative 5

SIGN CONVENTIONS—STATICS VS. DEFORMATION For beam deformations, signs are based on how forces deform the beam Axial forces that elongate are positive, ones that compress are negative A shear force in a beam is positive if it acts clockwise against the material, and negative if CCW Positive bending moment compresses upper part of beam, negative bending moment compresses the bottom part of beam 6

SIGN CONVENTIONS 7 So, for forces (loads) and bending moments that cause deformations: Both are positive axial loads Both are negative axial loads Positive shear forces and bending moments Negative shear forces and bending moments

DEFORMATION SIGN CONVENTION, CON’T 8

TWO EXAMPLES… 9

EXAMPLE 2—YOUR TURN 10

CALCULATE THE SHEAR FORCE V AND BENDING MOMENT M AT A CROSS SECTION LOCATED 0.5 M FROM THE FIXED SUPPORT OF THE CANTILEVER BEAM AB SHOWN IN THE FIGURE. A.V = 7.00 kN; M = 9.5 kNm B.V = 4.00 kN; M = -9.5 kNm C.V = 1.5 kN; M = 13 kNm D.V = 7.0 kN; M = -9.5 kNm 300

RELATIONSHIPS BETWEEN LOADS, SHEAR FORCES AND BENDING MOMENTS To the board… 12

REMINDERS HW#5 due Friday Feb 28 Read 4.5 for Friday Next exam is a week from Friday, March 7, in Ball Hall 210 Sections 3.1 – 3.8, and all of chapter 4. 13

QUESTIONS? 14