ME 323 - Mechanics of Materials - Lecture 4 - Introduction to design of deformable bodies

Oct 29, 2026

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Lecture 4 of ME 323 focuses on introducing the design of deformable bodies, starting from the representation of shear stress on a stress element and clarifying shear strain. The lecture reviews how shear stress and shear strain are related, then revisits stress on an inclined plane to decompose normal and tangential stress components for an axially loaded rectangular bar at angle θ. It motivates shear failure, then establishes objectives covering material properties review, material selection trade-offs, and factor-of-safety calculations using tensile testing and ASTM E8 guidance.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages14

Reading Time35 min

AccessFree to download

Objectives for today

Review material properties

Discuss material selection in design

Calculate factors of safety

If time permits: generalized stress and strain

Motivation and examples

Metals fail due to shear stress

Axial member with a weld line

Stress on an inclined plane

Material properties and testing

Tensile testing and ASTM E8

Stress-strain curves for aluminum alloys

Material selection and design trade-offs

Ashby diagram reference

Factors of safety

Using FS to account for uncertainty

Brittle vs ductile material approaches

ME 323 – Mechanics of Materials Lecture 4: Introduction to design of deformable bodies Joshua Pribe Fall 2019 From the end of last class… For the applied shear force V: • How do we represent the shear stress on a stress element? • What is the shear strain? • How are shear stress and strain related? Example from last class: Stress on an inclined plane For the axially loaded rectangular bar, what are the normal and tangential components of the stress acting on the plane given by the angle θ? Motivation: Metals typically fail due to shear stress Motivation: Axial member with a weld line Example from last class: Stress on an inclined plane For the axially loaded rectangular bar, what are the normal and tangential components of the stress acting on the plane given by the angle θ? Objectives for today • Review material properties • Discuss material selection in design • Calculate factors of safety • If time permits: introduce generalized stress and strain Steel: Nylon: Aluminum: Material properties: Tensile testing American Society of Testing and Materials (ASTM) Standard E8 governs tensile testing Measure load and displacement; convert to stress and strain Example: [https://www.youtube.com/watch?v=ipDZska5VN4](https://www.youtube.com/watch?v=ipDZska5VN4) Material properties Stress-strain curves for two aluminum alloys: How does composition affect the mechanical properties? Material properties Examples from the lecture book Material selection Typically a trade-off between weight and stiffness or strength 9 “Ashby diagram” from Shigley’s Mechanical Engineering Design Factors of safety (from pre-week video) Use a factor of safety to account for uncertainty in design 10 Factor of safety (FS) = Failure~~ ~~loActual~~ ~~loaadd 􀀡 1 Brittle Ductile Ductile materials (most metals): use the yield strength or ultimate strength FS = 􀁖􀁖acYtual~~ ~~ FS = 􀁗~~ ~~􀁗acUtual~~ ~~ use the ultimate strength Brittle materials: Axial loading: 􀁖U FS = ~~ ~~ 􀁖 actual FS = 􀁗~~ ~~􀁗acYtual~~ ~~ 􀁖U FS = ~~ ~~ 􀁖 actual Shear loading: Axial loading: Shear loading: FS = 􀁗~~ ~~􀁗acUtual~~ ~~

FAQs

How does the lecture represent shear stress and define shear strain?

It asks how shear stress is represented on a stress element and what the shear strain is. The goal is to connect these measures for deformable-body design.

What is decomposed when analyzing an axially loaded rectangular bar on an inclined plane?

The lecture revisits stress on an inclined plane and focuses on the normal and tangential stress components acting on the plane for a given angle θ.

How are factors of safety used differently for brittle versus ductile materials?

The lecture states that ductile materials use yield strength or ultimate strength, while brittle materials use ultimate strength. It introduces factor-of-safety expressions separately for different loading cases.

Oct 29, 2026

Upload by asba