Hi i need to carry out a propagation of Young's modulus to find the overall error for it. I have the readings and I have calculated the overall error for E (for Cantilever beam) but I'm not sure if it is correct. Pls could it be checked or could I have some help with it please. Thanks.

Mechanics of Materials (MindTap Course List)
9th Edition
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Barry J. Goodno, James M. Gere
Chapter9: Deflections Of Beams
Section: Chapter Questions
Problem 9.5.5P: A cantilever beam of a length L = 2.5 ft has a rectangular cross section {b = 4in,, h = Sin,) and...
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Hi i need to carry out a propagation of Young's modulus to find the overall error for it. I have the readings and I have calculated the overall error for E (for Cantilever beam) but I'm not sure if it is correct. Pls could it be checked or could I have some help with it please. Thanks.

Calculate overall error for E:
Relative uncertainity:
E= FL
31S
ΔΕ
SAL
1. 4. 20-8-20
第一。
E
4€ = 4/1
AE_AF_AS
E F
مام
AF = 0.01
F
for Cantilever Beam:
=
Absolore Uncertainity =
Δδ 0.01 = 3.24 x 10-³ (Error / uncertaining in measurement of deflection)
S
3.09
Relative Uncertaining
= 0.01 -(-3.24x10-³) = 0.01324
Absolute Uncertainity
for Simply - Supported Beam:
X 168 061-0972 = 22.251
= 0.01324 x 168 061-0972
100
Relative uncertai
100
ncertainity x measured value
}
€ = 168 061.0972 MPa
Transcribed Image Text:Calculate overall error for E: Relative uncertainity: E= FL 31S ΔΕ SAL 1. 4. 20-8-20 第一。 E 4€ = 4/1 AE_AF_AS E F مام AF = 0.01 F for Cantilever Beam: = Absolore Uncertainity = Δδ 0.01 = 3.24 x 10-³ (Error / uncertaining in measurement of deflection) S 3.09 Relative Uncertaining = 0.01 -(-3.24x10-³) = 0.01324 Absolute Uncertainity for Simply - Supported Beam: X 168 061-0972 = 22.251 = 0.01324 x 168 061-0972 100 Relative uncertai 100 ncertainity x measured value } € = 168 061.0972 MPa
Error propagation (from lective notes)
E = f(L, F, b, S, [F/Smax])
For a Cantilever beam:
E = FL³
31Smax
2
Equation: (62)² + (6 A)² + (588)² + (doc)"
f
=
F=2N L=360mm S = 3,09mm
E = 2 × (360³)
=168 061. 0972 MPa
3x59.85x3.09
Uncelhaining onb = ±0.001
uncertainity on L = ± 0.05 Em or ± 0.5mm
on
Transcribed Image Text:Error propagation (from lective notes) E = f(L, F, b, S, [F/Smax]) For a Cantilever beam: E = FL³ 31Smax 2 Equation: (62)² + (6 A)² + (588)² + (doc)" f = F=2N L=360mm S = 3,09mm E = 2 × (360³) =168 061. 0972 MPa 3x59.85x3.09 Uncelhaining onb = ±0.001 uncertainity on L = ± 0.05 Em or ± 0.5mm on
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