Lab #4 Report due TODAY
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
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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
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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 = R 2 = F
V = 0 in middle span
M = -bF = constant
in middle span
Pure Bending
Pure Bending
Material 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
x = -y/
𝑤𝑡 3
𝐼=
12
1 𝑀
= =
𝜌 𝐸𝐼
x = Ex = -Ey/
Sagital Method to find the
Radius of Curvature 
h × (2 - h) = a2
2h – h2 = a2
If h <<  and a then
1 2ℎ 𝑀
= = 2 =
𝜌 𝑎
𝐸𝐼
M = bF
𝑏𝐹𝑎2
ℎ=
2𝐸𝐼
Shear Force & Bending Moment
Diagrams
R1 = R 2 = F
V = 0 in middle span
M = -bF = constant
in middle span
Pure Bending
Data Sheet
Processing Data
𝑤𝑡 3
𝐼=
12
ℎ=
𝑧2 −
𝑧1 + 𝑧3
2
25.4
𝑎 2 + ℎ2
𝜌=
2ℎ
Plotting Multiple Lines
Adding Data for another Line
h versus W Line Fits
𝑏𝐹𝑎2
ℎ=
2𝐸𝐼
Fitting Straight Line
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LINEST function (y = m*x + b)
Gradient m =
INDEX( LINEST(y-values, x-values, False, True), 1)
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b=0
m
Coefficient r2 =
INDEX( LINEST(y-values, x-values, False, True), 3)
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b=0
r2
Table of a2 and gradients
𝑏𝑎2
𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
2𝐸𝐼
Plot of Gradient versus a2
𝑏𝑎2
𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 =
2𝐸𝐼
Calculating Elastic Modulus E
𝑏
𝑠𝑙𝑜𝑝𝑒 =
2𝐸𝐼
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