Mechanical Engineering Department

WORCESTER POLYTECHNIC INSTITUTEMECHANICAL ENGINEERING DEPARTMENT

STRESS ANALYSISES-2502, D’2020

17 April 2020

We will get started soon...

Mechanical Engineering Department

STRESS ANALYSISES-2502, D’2020

WORCESTER POLYTECHNIC INSTITUTEMECHANICAL ENGINEERING DEPARTMENT

We will get started soon...

Lecture 14: Unit 6: tension/compression of slender

longitudinal bars: stress concentrations

17 April 2020

Mechanical Engineering Department

Instructor: Cosme FurlongHL-152

(774) 239-6971 – Texting WorksEmail: cfurlong @ wpi.edu

http://www.wpi.edu/~cfurlong/es2502.html

General information

Teaching Assistant: Zachary ZolotarevskyEmail: zjzolotarevsky @ wpi.edu

Mechanical Engineering Department

Stress concentrations

Ripping open candy wrap with the help of

stress concentration

Stress

concentrations

appear here

Zigzag edges added to

amplify appliedstresses

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Stress concentrations: stress “flow”

Reducing stress

concentration:

rounding edges

Stress concentration on:

sharp edgesReducing stress concentrations

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Designing to minimize stress concentrations

Initial design Improved design

Modifications to reduce stress concentrations at a sharp corner

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Stress concentrationsAxially loaded component with a hole: stress concentration factor

avg

max

KStress concentration factor:

Stresses

distribution

Mechanical Engineering Department

Stress concentrationsAxially loaded component with a hole: stress concentration factor

𝑃 = න𝜎 𝑑𝐴

A @ a-a

Internal balancing

force at a-a

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Stress concentration factorAxially loaded component with a hole

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Stress concentrationsAxially loaded component with edges: stress concentration factor

avg

max

KStress concentration factor:

Stresses

distribution

Mechanical Engineering Department

Stress concentrationsAxially loaded component with edges: stress concentration factor

𝑃 = න𝜎 𝑑𝐴

A @ a-a

Internal balancing

force at a-a

Mechanical Engineering Department

Stress concentration factorAxially loaded component with edges

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Axial load: example O

The A-36 steel plate has a thickness of 12 mm. If there are shoulder

fillets at B and C, and Allow = 150 MPa, determine the maximum axial

load P that it can support. Calculate its elongation, neglecting the effect

of the fillets.

Approach:

1) Determine stress

concentration factors

2) Compute maximum

load

3) Compute elongation

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Inelastic axial deformationPlastic deformations

Model: elastic perfectly

plastic behavior

Mechanical Engineering Department

Inelastic axial deformationPlastic deformations

Distribution of internal stresses

as load increases

(a)

Elastic

deformations(b)

Elastic + plastic

deformations

(c)

Plastic

deformations

Mechanical Engineering Department

Reading assignment

• Chapters 3 and 4 of textbook

• Review notes and text: ES2001, ES2501

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Homework assignment

• As indicated on webpage of our course