General Review - TARKIAHAerospace Structural Analysis M. F. GHANAMEH 2017-2018-3-Course Organization Lecture Monday 08:30 - 10:30 AM Tutorial Gr A :Thursday 10:30 - 12:30 AM

Aerospace Structural Analysis

M. F. GHANAMEH

2017-2018-1-

Lecture 1

General Review

Mohamad Fathi GHANAMEH

Structural Analysis


M. F. GHANAMEH

2017-2018-2-

✓Course overview

✓Review some of the important

principles of Mechanics of Materials.

✓Concepts of loads, normal and shear

stress and strain; and deformation.

Lecture Topics


M. F. GHANAMEH

2017-2018-3-

Course Organization

Lecture

Monday 08:30 - 10:30 AM

Tutorial

Gr A :Thursday 10:30 - 12:30 AM

Gr B: Thursday 08:30 - 10:30 AM


M. F. GHANAMEH

2017-2018-4-

Instructor

Mohamad Fathi GHANAMEH

[email protected]

Course Documentation and Support

http://ghanameh.tarkiah.com/index.php/courses/structural-analysis

Office Hours

Monday 16:00 - 18:00 PM

Course Organization

mailto:[email protected]

http://ghanameh.tarkiah.com/index.php/courses/structural-analysis


M. F. GHANAMEH

2017-2018-5-

✓ R. C. Hibbeler, Mechanics Of Materials, 8th Edition, Pearson Prentice Hall,

2011.

✓ R. C. Hibbeler, Structural Analysis, 8th Edition, Pearson Prentice Hall, 2012.

✓ T.H.G.-Megson, Introduction to Aircraft Structural Analysis, 4th Edition,

Elsevier, 2007.

Textbook & References


M. F. GHANAMEH

2017-2018-6-

Review the solution

Carry out the solution

Plan the solution

For a given problem, three steps are used to solve the problems

correctly:

Problem-solving Procedures


M. F. GHANAMEH

2017-2018-7-

Loading

Materials

Geometry

Structural Analysis

Structural Analysis


M. F. GHANAMEH

2017-2018-8-

• Studies the internal effects of stress and strain in

structure that is subjected to external loadings.

• study of the structure’s stability when it is

subjected to defined loadings

Structural Analysis


M. F. GHANAMEH

2017-2018-9-

mechanical Structure

Load – stress – strain

internal Loading

Strain

StressExternal Loading

Strain is a measure of the

deformation of the

structure or its

components

Stress is associated with

the strength of the

material from which the

structure is made


M. F. GHANAMEH

2017-2018-10-

External Loading

External Loads

Surface Forces Body Forces

Concentrated Distributed

.W m g


M. F. GHANAMEH

2017-2018-11-

The components and acting of both normal and

perpendicular to the sectioned area must be considered,

Four different types of resultant loadings can then be defined

as follows:

Internal Resultant Loadings


M. F. GHANAMEH

2017-2018-12-

• Procedure for Analysis

The resultant internal loadings at a point located on the section

of a body can be obtained using the method of sections. This

requires the following 3 steps:

1. Support Reactions.

2. Free-Body Diagram.

3. Equations of Equilibrium.



M. F. GHANAMEH

2017-2018-13-

✓ Decide which segment of the body is to be considered.

✓ If the segment has a support or connection to another body,

then before the body is sectioned, it will be necessary to

determine the reactions acting on the chosen segment.

✓ To do this draw the free-body diagram of the entire body

and then apply the necessary equations of equilibrium to

obtain these reactions.

1. Support Reactions



M. F. GHANAMEH

2017-2018-14-

1. Support Reactions



M. F. GHANAMEH

2017-2018-15-

✓ Keep all external distributed loadings, couple moments, torques,

and forces in their exact locations, before passing an imaginary

section through the body at the point where the resultant internal

loadings are to be determined.

✓ Draw a free-body diagram of one of the “cut” segments and

indicate the unknown resultants N, V, M, and T at the section.

These resultants are normally placed at the point representing the

geometric center or centroid of the sectioned area.

✓ If the member is subjected to a coplanar system of forces, only N,

V, and M act at the centroid.

✓ Establish the x, y, z coordinate axes with origin at the centroid and

show the resultant internal loadings acting along the axes.

2. Free-Body Diagram



M. F. GHANAMEH

2017-2018-16-

✓ Moments should be summed at the section, about each of the

coordinate axes where the resultants act. Doing this eliminates

the unknown forces N and V and allows a direct solution for

M and T.

✓ If the solution of the equilibrium equations yields a negative

value for a resultant, the assumed directional sense of the

resultant is opposite to that shown on the free-body diagram.

3. Equations of Equilibrium



M. F. GHANAMEH

2017-2018-17-

Equilibrium of a body requires both:

a balance of forces, to prevent the body from translating

or having accelerated motion along a straight or curved path, and

a balance of moments, to prevent the body from

rotating. These conditions can be expressed mathematically by

two vector equations

0

0o

F

M

0, 0, 0

0, 0, 0

x y z

x y z

F F F

M M M

0, 0

0

x y

o

F F

M

planar system

3D system


3. Equations of Equilibrium


M. F. GHANAMEH

2017-2018-18-

The state of stress is characterized by three components

acting on each face of the element.

Stress

0lim z

zA

F

A

0lim x

zxA

F

A

zxspecifies the

orientation of the

area

indicate the axes

along which shear

stress acts.

, ,x x y y z z

, ,zy zy xy xy zx zx

, ,zy yz xy yx zx xz


M. F. GHANAMEH

2017-2018-19-

If the load applied to the member is linearly related to the stress

developed within the member, the factor of safety is the ratio of the

failure stress 𝜎𝑓𝑎𝑖𝑙 (or 𝜏𝑓𝑎𝑖𝑙) to the allowable stress 𝜎𝑎𝑙𝑙𝑜𝑤 (or

𝜏𝑎𝑙𝑙𝑜𝑤 ); that is,

Allowable Stress

.fail

allow

F S

.

fail

allow

F S

. 1F S


M. F. GHANAMEH

2017-2018-20-

Normal Strain

s s

s

Strain

Deformation

Shape Size

Shear Strain

t

lim2

ntB A along nC A along


M. F. GHANAMEH

2017-2018-21-

From this curve

we can identify

four different

ways in which the

material behaves,

depending on the

amount of strain

induced in the

material.

Properties of Materials


M. F. GHANAMEH

2017-2018-22-

Properties of Materials

.E

Poisson’s Ratio

lat

long

longitudinal elongation (positive strain)

lateral contraction (negative strain)

.G

Hooke’s Law

Normal Stress Shear Stress

2 1

EG


M. F. GHANAMEH

2017-2018-23-

Loading State

Loading state

Axial Tension

Compression

Buckling

Bending

Torsion

The load applied along

its longitudinal axis

The load applied

perpendicular to its

longitudinal axis

Torque is a moment that

tends to twist a member

about its longitudinal axis


M. F. GHANAMEH

2017-2018-24-

Axia

lT

ors

ion

Ben

din

g

Loading State


M. F. GHANAMEH

2017-2018-25-

Axia

lT

ors

ion

Ben

din

g

Loading State

int. 0 0. .

x l x l

x xP cont cont

int. 0 0. .

x L x L

x xT cont cont

int. 0 0 0. ( ) ( )

x L x L x L

x x xM cont f x f x

int. 0 0. .

x L x L

x xV cont cont


M. F. GHANAMEH

2017-2018-26-

Axia

lT

orsi

on

Ben

din

g

Loading State

.

.

P L

E A

.

.

P L

E A

P

A

max

.T c

J

0

.c

T

J

.

.

T L

J G .

.

T L

J G

max

.M c

I

.yy h

y h

M

I

21 1(x)dx; (x)dxM M

EI EI

11

22

t tt Q

t Qt t

VQ

It


M. F. GHANAMEH

2017-2018-27-

Possible boundary conditions


M. F. GHANAMEH

2017-2018-28-

Torsi

on

Polar moment of inertia of the shaft’s cross-sectional area about

the shaft’s longitudinal axis

Solid Shaft4

.2

Jc

Tubular Shaft.

4 4

0.2

iJc c

Loading State


M. F. GHANAMEH

2017-2018-29-

Ben

din

g

Loading State

2.A

I y dA

The integral represents the moment of inertia of the cross-sectional

area about the neutral axis

3

(z) (y).

12z

a bI

.i i

i

y Ay

A

.dI I A 4

4zI r

Circular Rectangular Composite area


M. F. GHANAMEH

2017-2018-30-

Ben

din

g

Loading State

tan tanz

y

I

I

Moment Arbitrarily Applied

.z .y z

y z

M M y

I I

Orientation of the Neutral Axis

Documents

General Review - TARKIAHAerospace Structural Analysis M. F. GHANAMEH 2017-2018-3-Course Organization Lecture Monday 08:30 - 10:30 AM Tutorial Gr A :Thursday 10:30 - 12:30 AM