Lecture 18 – Review for Exam 1

Instructor: Prof. Marcial Gonzalez

Fall, 2021ME 323 – Mechanics of Materials

Reading assignment: Lectures 1-14

News: Ready for the exam?

Exam 1- Wednesday October 6th , 8:00-10:00 p.m., room WTHR 200

(please arrive 15 minutes before the exam and bring a picture ID)

- Formula sheet will be provided

- You will scan your exam and submit to Gradescope – come prepared!

- No lecture on Wednesday

- Start working on the lecture book!

Announcements

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https://www.purdue.edu/freeform/me323/additional-lecture-notes-2/prof-gonzalez-730/

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Summary of topics

- State of stress vs. state of strain (generalized Hooke’s law)- Bolted and pinned joints. Factor of safety.- Axial deformations (statically indeterminate problems)- Thermal loads- Torsional deformations (statically indeterminate problems)- Truss structures (statically indeterminate problems)- Shear force and bending moment diagrams

- Lectures 1–14

Review

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Equation sheet for Exam 1

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Direct shear: Bolted joint & Pinned joint

Shear stress and strain

Average shear stress: Average shear stress:

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Axial deformation (summary)- Geometry of the solid body: straight, slender member with cross section that

is either constant or that changes slowly along the length of the member.- Kinematic assumptions: cross sections, which are plane and are perpendicular

to the axis before deformation, remain plane and remain perpendicular to the axis after deformation. In addition, cross sections do not rotate about the axis.

- Material behavior: isotropic linear elastic material; small deformations.

- Equilibrium:

Axial deformation

Strain:

Elongation:

Homogeneous:

Homogeneous:

Homogeneous, constant cross section, no body forces, thermal load:

Homogeneous, loaded with body forces:

for trusses …

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Torsional deformation (summary)- Geometry of the solid body: straight, slender member with circular cross

section that changes slowly along the length of the member.- Kinematic assumptions: the axis remains straight and inextensible. Cross

sections, which are plane and are perpendicular to the axis before deformation, remain plane and perpendicular after deformation. Radial lines remain straight and radial as the cross section rotates about the axis

- Material behavior: isotropic linear elastic material; small deformations.

- Equilibrium: (torque-twist equation)

Torsion

Shear strain

Total angleof rotation

Homogeneous:

Homogeneous:

Homogeneous, constant cross section:

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Axial deformations

Review problems

Problem 9) Compatibility conditionsFor a small angle of rotationand member AD rigid:

staticallyindeterminate

structures

Problem 10) Compatibility conditions

1) Free body diagram2) Equilibrium equations3) Force-displacement behavior4) Compatibility conditions5) Solve for unknowns

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Indeterminate trusses

Review problems

1) Free body diagram2) Equilibrium equations3) Force-displacement behavior4) Compatibility conditions5) Solve for unknowns

staticallyindeterminate

structures

Problems 12-13) Compatibility conditions

with B fixed (angle measured at D from x-axis to

the member counterclockwise)

with C fixed

with D fixed

Review problems

Torsional deformations

Example 16Determine the maximum shear stress in the steel and the maximum shear stress in the aluminum.

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Example 17Determine the strain energy density.Determine the total rotation at D.Determine the state of stress at given points.

Example 18Select dimensions that fulfill design constrains

Equilibrium relationships- Sign convention!

Equilibrium of beams

These are all positive external loads and couples

Note: become familiar with sign convention for external loads and for internal reactions.11

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Best of luck in the exam!

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Review session – Exam 1

From the survey …1- Indeterminate torsional loads2- State of stress in shafts3- Indeterminate axial loads4- Indeterminate trusses