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MSE 221 Review (Statics)

Ch. 1 Two unit systems and conversion

Ch. 2 Statics of Particles

Force addition and decomposition using triangles, polygon rule, and decomposition to x and y

3-D force vectors and particle equilibrium

Ch. 3 Equivalent systems of forces

Moment

2

Ch. 4 Equilibrium of rigid bodies

Free body diagram

Reactions and supports

00 FrMF O

or

000

000

zyx

zyx

MMM

FFF

Ch. 6 Analysis of structures

Truss, frame, machine

Methods of joints, method of sections, multi-component analysis

Ch. 5 Centroids, 1st moment of area

• Areas/volumes and the centroids of common shapes

• Properties of symmetry

• Theorems of Pappus-Guldinus

• Composite areas/volumes

• Distributed loads

Ch. 9 2nd Moment of area (moments of inertia and mass)

Composite areas

dAxIdAyI yx22

xy IIdArJ 2

0

2AdII

dmxzdmrI y

222

dmyxI

dmzyI

z

x

22

22 2mdII

dWyWy

dWxWx

dLyLy

dLxLx

dAyAy

dAxAx

dVyVy

dVxVx

3

Mechanics of Materials

Ch. 1 Introduction to stresses

Normal stress, shear stress, bearing stress

Factor of safety

Chs. 2-4 Axial loading, Torsion, Pure Bending

Axial Loading Torsion Pure Bending

Basic Equations

Basic Equations

Basic Equations

Thermal Stress

Gears

Total Force of an Area

, where

is the centroidal coordinate of the shaded portion (area) and A* is its area.

Generalized Hook’s Law

Shear Strain

Statically indeterminacy

Power transmission

Statically indeterminacy

General Case of Eccentric Axial Loading

Stress Concentration

Stress Concentration

(J,c for smaller diameter

shaft)

Stress Concentration

(c, I for critical

section)

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Ch. 5 Shear and Moment Diagram

D

C

x

xCD dxwVV

wdx

dV

D

C

x

x

CD dxVMM

Vdx

dM

Ch. 9 Beam deflection

• Substituting and integrating,

21

00

1

0

2

21

CxCdxxMdxyEI

CdxxMdx

dyEIEI

xMdx

ydEIEI

xx

x

Continuity condition

Superposition using Appendix D

Labs:

1. Measuring torsion and bending using simple set-up

2. Measuring torsion and bending using strain gauge

Integration for problems solving

- Be able to calculate and analyze forces, moments, and equilibrium conditions for 2-D and 3-D

rigid bodies, including trusses, frames, and machines

- Be able to apply the loading conditions (axial loading, torsion, bending, and simple shearing) to

solve for stresses in a component

- Be able to draw shear and moment diagram for beams, calculate beam deflections, and use the

info for beam design