02A – Cantilever Load Cell
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08/16/22
Analaysis
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Summary
The following report presents various analyses for a cantilever load cell, summarized below. All elements are
quadratic (beam and hexahedrals) with a global size of 0.0525”. The composite plate is E-Fiberglass/Epoxy, FVR
= 67%. The contacting plates are rigid. The beam connections are low alloy steel. Deviations from beam theory
are explained for each analysis.
1. 2D analysis of beam elements.
2. 3D analysis of solid composite plate bonded to rigid plates.
3. 3D analysis of solid composite plate with holes bonded to rigid plates.
4. 3D analysis of solid composite plate with holes connected to rigid plates via elastic beam connections
(representing screws).
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Analaysis
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b
Proximal Plate Reactions
P over 2.05”
𝑃 = 180 𝑙𝑏𝑓
𝑎 = 2.83 𝑖𝑛
𝑏 = 1.415 𝑖𝑛
𝑅1 = 𝑃
𝑅1 = 180 𝑙𝑏𝑓
a
𝑀1 = 𝑃𝑏
𝑀1 = 254.7 𝑙𝑏𝑓 ∙ 𝑖𝑛
P over 2.05”
M1
R1 over 0.04”
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Analaysis
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b
Composite Reactions
P over 2.05”
𝑃 = 180 𝑙𝑏𝑓
𝑎 = 2.83 𝑖𝑛
𝑏 = 1.415 𝑖𝑛
𝑅1 = 180 𝑙𝑏𝑓
𝑀1 = 254.7 𝑙𝑏𝑓 ∙ 𝑖𝑛
a
𝑅2 = 𝑅1
𝑅2 = 180 𝑙𝑏𝑓
R1 over 0.04”
෍ 𝑀𝑅2 = 𝑀2 − 𝑀1 + 𝑅1 𝑎 = 0
𝑀2 = −254.7 𝑙𝑏𝑓 ∙ 𝑖𝑛
M2
M1
R2 over 0.04”
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Analaysis
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Materials
E-Fiberglass/Epoxy, FVR = 67%
Low Alloy Steel
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Analaysis
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Beam Elements
Shear
Beam Width (into slide) = 2”
Beam Height = 0.21”
Moment
Deflection
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Analaysis
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Discussion of Previous Slide
• Beam geometry allows for Euler-Bernoulli deflection.
• Though the material is orthotropic, the x-direction material properties are dominant and results are equivalent
to isotropic bending.
• All diagrams verified by hand calcs.
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Analaysis
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Solid Elements, Bonded Contacts
y-axis direction
Bonded Contact Surfaces
x-axis direction
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Analaysis
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Discussion of Previous Slide
• Deflection is very close to beam results
• Minimum normal stress (maximum compressive bending stress) is a singularity due to contact with sharp
corner of plates.
• Maximum normal stress is ~14% less than beam results. Primarily due to the bonded contact where beam is
supported by distributed load, thus there is a decrease in moment arm and a decrease in moment in the solid.
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Analaysis
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Solid Elements with Holes, Bonded Contacts
y-axis direction
Bonded Contact Surfaces
x-axis direction
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Discussion of Previous Slide
• Deflection has increased compared to the previous analysis due to the decrease in stiffness at the hole
locations.
• Minimum normal stress (maximum compressive bending stress) is a singularity due to contact with sharp
corner of plates.
• The increase in maximum normal stress is local to the hole locations. The probed value of 16,077 psi away
from the holes is more realistic, though is still lower than beam results due to the bonded contact and decrease
in moment arm.
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Analaysis
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Solid Elements with Holes, Beam Connections
Beam Connections
y-axis direction
No Separation Contact Surfaces
x-axis direction
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Discussion of Previous Slide
• Deflection has grown compared to the previous analysis due to the elastic beam elements able to bend.
• Minimum normal stress (maximum compressive bending stress) is a singularity due to contact with sharp
corner of plates.
• The increase in maximum normal stress compared to previous analysis is due to the increase in deflection.
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Analaysis
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