Strength of MaterialsDr. Fathy Elnaggar

Strength of Materials

Civil Engineering Department

By

Dr. Fathy Elnaggar

Text Book 

1. Mechanics of Materials, 2nd ed,  by R.C. Hibbeler, pub. by Prentice Hall.

2. Ferdinand P. Beer, E. Russell Johnston, John T. DeWolf, "Mechanics of Materials", McGraw-Hill Higher Education, Last Edition

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Strength of MaterialsDr. Fathy Elnaggar

3. Ansel C. Ugural, "Mechanics of Materials", John Wiley & Sons, Last Edition.

Grading and evolution5% Quizzes and Home work10% Quizzes and Home work20% First midterm exam15% second midterm exam50% Final exam

Objectives: To provide an introduction to materials and solid mechanics including the study and quantitative determination of stress, strain, stability, deflection.To learn analyze structures and predict failure of material under a variety of loading types.To understand how altering geometry and shape can be used to minimize stress.

Week Date Event 1 Sunday January 26

2 Sunday February 2

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Strength of MaterialsDr. Fathy Elnaggar

3 Sunday February 9

4 Sunday February 16 February 118 Quizz 1

5 Sunday February 23

6 Sunday March 2March 4 Quizz 2

7 Sunday March 9

8 Sunday March 16 Test 1

9 Sunday March 23 Vacation

10 Sunday March 30April 1 Quizz 3

11 Sunday April 6

12 Sunday April 13 Test 2

13 Sunday April 20

14 Sunday April 27April 29 Quizz 4

15 Sunday May 4

16 Sunday May 11

17 Sunday May 18 Review

CE 241: Strength of Materials Lecture 01: Internal Forces and Axial Stress

Following today's class you should be able to:-- find internal forces of a body-- calculate axial stress for simple loadings.

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Strength of MaterialsDr. Fathy Elnaggar

Statics Review: For a Rigid Body to be in equilibrium:

and

To solve Equilibrium problems start by drawing the Free Body Diagram.

1) Isolate the body from the environment

2) Show all concentrated forces and moments acting on the body. Label known values. Provide variables for unknown forces and moments.

3) Show simple geometry.

4) Apply the equilibrium equations to the body

5) Solve equations for unknowns.

Common support types:

If a support has the ability to stop a body's motion along a given direction or if it can stop rotation about an axis, then a support reaction must be included on the diagram.

Finding Internal Loads:

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Strength of MaterialsDr. Fathy Elnaggar

Axial Force (N): a force which acts normal to or perpendicular to a defined internal plane.

Shear Force (V): a force which acts parallel to a defined internal plane.

Torsional Moment or Torque (T): a moment of force acting about an axis which is normal to or perpendicular to a defined internal plane.

Bending Moment (M): a moment of force acting about an axis which lies parallel to a defined internal plane.

The stress set up by each of these internal loading are found using different stress equations. Together, they represent the combined total stresses acting in a body and each contributes to the total stress load of a body.

Examples to explaining of Internal Loads.

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NP'

Strength of MaterialsDr. Fathy Elnaggar

Axial Load, N

Shear Load, V

Torque, T Bending Moment, M

Example 1: Find the Internal Reactionsat point C.

Start by finding thethe support reactions.

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A

2m3m2m1m

6 kN5 kN4 kN

B

1m

C

Strength of MaterialsDr. Fathy Elnaggar

Next find the internal reactions:

Using the Right side:

Average Normal Stress:

The normal stress represents the force per unit area that a normal force exerts on the internal plane of the material.

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FBD

AFAx

6 kN5 kN4 kN

BC

FAy FB

1m

AFAx

6 kN5 kN4 kN

BC

FAy FB

M

NV FBD

FBD

P=500 lb

dia = 0.75 in=c

Strength of MaterialsDr. Fathy Elnaggar

This is found using

Where, σ is the normal stress in units such as lbf/in2 or N/m2

N is the axial force normal to the surface

A is the cross sectional area.

Stress which extends the body is considered tensile stress and is considered positive (+).

Stress which compresses the body is called compressive stress and is considered negative (-).

This model for normal stress is based on several assumptions:-- The body is expected to deform uniformly-- Localized distortions caused by the external loads are ignored.-- The load is applied along the centroidal axis-- The body is made up of homogeneous material and the material has isotropic properties.

Example 3:

A 500 lb force is applied to a metal rod of 0.75 inch diameter.

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Strength of MaterialsDr. Fathy Elnaggar

Determine the average normal stressan acceptable distance away from theapplied load and fixed support.

Normal stress is given by

where

Therefore

Homework Set 01

Problem 1:9:Determine the resultant internal loadings on the cross sections located through points F and G of the frame.___________________________________________________________________________Solution:

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P=500 lb

σ

Strength of MaterialsDr. Fathy Elnaggar

Problem 1.39The thrust bearing is subjected to the loads shown. Determine the average normal stress developed on the cross section at B, C, and D. Sketch the results on a volume element located at each section.

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Strength of MaterialsDr. Fathy Elnaggar

Problem 1.58The bars of the truss each have a cross sectional area of 1.25 sq. in. Determine the average normal stress in each member due to the loading P = 6 kip. State whether the stress is tensile or compressive.

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