Lab #4 Report due TODAY Individual Data Processing and

Individual Write Up Lab #4 Report is due TODAY by

midnight Answer Multiple Choice Questions

ONLINE TODAY Answer Student Survey ONLINE TODAY Submit the Lab Report #4 in the drawer

labeled “Strength of Materials I Lab” beneath M. E. Mail Folders

Theory of Pure Elastic Bending Four Point Bending Configuration Shear Force and Bending Moment

Diagrams Stresses and Deformations in Pure

Bending Sagital Method to find Radius of

Curvature Determine Elastic Modulus of material Comparison to handbook value and

previous Lab #4 result

Four Point Bending Setup

Shear Force & Bending Moment Diagrams

R1 = R2 = F

V = 0 in middle span

M = -bF = constantin middle spanPure

Bending

Pure BendingMaterial Assumptions Homogeneous Isotropic

Geometry/Load Assumptions

X-section has a plane of symmetry

Bending moment applied in that plane

Deformation Grids

Neutral Axis and Strain(elastic and plastic range)

Elastic Strain & Stress Distribution

=1𝜌

=𝑀𝐸𝐼

x = -y/ x = Ex = -Ey/

𝐼=𝑤𝑡3

12

Sagital Method to find theRadius of Curvature

h × (2 - h) = a2

2h – h2 = a2

If h << and a then

M = bF

Shear Force & Bending Moment Diagrams

R1 = R2 = F

V = 0 in middle span

M = -bF = constantin middle spanPure

Bending

Data Sheet

Processing Data

h=[𝑧 2− 𝑧1+𝑧 32 ]

25.4𝜌=𝑎2+h2

2h

𝐼=𝑤𝑡3

12

Plotting Multiple Lines

Adding Data for another Line

h versus W Line Fits

h=𝑏𝐹𝑎2

2𝐸𝐼

Fitting Straight Line

LINEST function (y = m*x + b) Gradient m = INDEX( LINEST(y-values, x-values, False, True), 1)

Coefficient r2 =INDEX( LINEST(y-values, x-values, False, True), 3)

b = 0

b = 0

r2

m

Table of a2 and gradients

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡= 𝑏𝑎2

2𝐸𝐼

Plot of Gradient versus a2

𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡= 𝑏𝑎2

2𝐸𝐼

Calculating Elastic Modulus E

𝑠𝑙𝑜𝑝𝑒=𝑏2𝐸𝐼

Materials Properties Tables

Fit the spreadsheet on 2 pages

Lab #4 Report due TODAY Individual Data Processing and

Individual Write Up Lab #4 Report is due TODAY by

midnight Answer Multiple Choice Questions

ONLINE TODAY Answer Student Survey ONLINE TODAY Submit the Lab Report #4 in the drawer

labeled “Strength of Materials I Lab” beneath M. E. Mail Folders