INTRODUCTION TO MECHANICS OF MATERIALS

(INGE 4019)

Pablo G. Caceres-Valencia (B.Sc., Ph.D., U.K.)

AssessmentThe course will be assessed in the following manner:

1st Exam 25%

2nd Exam 30%

Quizzes* 30%

Others** 15% (*)

(*) Date due WebCT or Moodle Quizzes and Pop‐Quizzes (max‐6). Missed quizzes will be graded with zero. Lack of access to WebCT or Moodle is not an excuse for not submitting your answers. 

(**) Class participation and Attendance. After the third missed class, one point will be deducted in the final grade for each missed class (up to 15 points). 

GENERAL INFORMATION

Course Number INGE 4019

Course Title Introduction to Mechanics of Materials

Credit Hours 4

Instructor Dr. Pablo G. Caceres-Valencia

Office Lucchetti L-212, Extension 2358

Office Hours M-W from 9-12am and 1-3pm

e-mail pcaceres@me.uprm.edu

Web-site http://academic.uprm.edu/pcaceres

Grades Final Grade Range Final Letter Grade

100 – 90 A

89 – 80 B

79 – 70 C

69 – 60 D

59 ‐ 0 F

AttendanceAttendance and participation in the lecture are compulsory and will be considered in the grading. Students should bring calculators, rulers, pen and pencils to be used during the lectures. Students are expected to keep up with the assigned reading and be prepared toanswer questions on these readings during lecture and for the pop‐quizzes. Please refer to the Bulletin of Information for Undergraduate Studies for the Department and Campus Policies.

Monday Wednesday Monday Wednesday

08/12Introduction

08/17Mech.Prop.

08/31Statically

Indetermined

09/14Torsion

09/28Shear and Bending

10/12Holiday

10/26Hooke’s Law

11/09Combined Loadings

11/23Combined Loadings

08/19Linear Elasticity

08/24Axial Loads

08/26Axial Loads

09/02Thermal Effects

Tuesday 09/07Stresses on Inclined

Planes

09/09Stress Concentration

09/16Thin Walled Tubes

09/211st Exam

09/23Holiday

09/30Shear and Bending

10/05Principal Stresses

10/07Mohr’s Circle

10/14Triaxial Stresses

10/19Plane Stresses

10/21Plane Stresses

10/28Plane Strain

11/02Plane Strain

11/04Elasticity

11/11Holiday

11/16Combined Loadings

11/182nd Exam

11/25Deflection of Beams

11/30Deflection of Beams

12/02Deflection of Beams

Tentative Dates

Outcomes

Upon the completion of the course the student should be able to:

• Calculate the principal stresses and strains in a loaded component

• Solve problems using stress transformation and Mohr’s circle

• Apply Hooke’s law for plane stress and plane strain

• Calculate stresses in thin walled spherical or cylindrical pressure vessels

• Calculate the stresses produced by combined axial, bending and torsional loads

TexbooksJames M. Gere and Barry J. Goodno, Mechanics of Materials, 7th Edition, CengageLearning.

My lecture notes are available in the web at

http://academic.uprm.edu/pcaceresSee syllabus of the course for recommended books.

ExamsAll exams will be conducted during lecture periods on the specified dates. There will be no final exam. Neatness and order will be taking into consideration in the grading of the exams. Up to ten points can be deducted for the lack of neatness and order. You must bring calculators, class notes and blank pages to the exams.

Review of StaticsMechanics of materials is a branch of mechanics that develops relationships between the external loads applied to a deformable body and the intensity of internal forces acting within the body as well as the deformations of the body.

Equations of equilibrium (i.e., statics) are mathematical expressions of vector relationships showing that for a body not to translate or move along a path then ΣF = 0 . For a body not to rotate, ΣM = 0.

StressStress has two components, one acting perpendicular to the plane of the area and the other acting parallel to the area. Mathematically, the former component is expressed as a normal stress which is the intensity of the internal force acting normal to an incremental area such that:where +σ = tensile stress = "pulling" stress and -σ = compressive stress = "pushing“ stress.

The latter component is expressed as a shear stress which is the intensity of the internal force acting tangent to an incremental area such that:

COMPRESSION(*squeezing)

TENSION(*stretching)

Prismatic bar in tension: (a) free-body diagram of a segment of the bar, (b) segment of the bar before loading, (c) segment of the bar after loading, and (d) normal stresses in the bar.

Prismatic bar = Section does not change in the length of the bar

-ve

+ve

strain- normal

stress

==

==

L

AP

δε

σ

L

AP

AP

δε

σ

=

==22

LL

AP

δδε

σ

==

=

22

Normal Stress and Normal Strain

Uniform Normal Stress

©2001 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license.

Uniform stress distribution in a prismatic bar: (a) axial forces P, and (b) cross section of the bar.

Stresses are constant over the cross sectional area.

To have uniform stresses (tension or compression) over the cross-section area (A), the axial force must act along the centroid.

A

Ayy

AAx

x ∫∫ ==δδ

Does the material resist the applied force?

What is the relationship between the stress applied and the deformation?

Tensile Testing• The sample is pulled slowly• The sample deforms and then fails• The load and the deformation are measured

Force

Extension or change in length

Determine the deformation of the steel rod shown under the givenloads.

in.618.0 in. 07.1

psi1029 6

==

×= −

dD

E

221

21

in 9.0

in. 12

==

==

AA

LL

23

3

in 3.0

in. 16

=

=

A

L

• Apply free-body analysis to each component to determine internal forces,

lb1030

lb1015

lb1060

33

32

31

×=

×−=

×=

P

P

P

• Evaluate total deflection,

( ) ( ) ( )

in.109.75

3.0161030

9.0121015

9.0121060

10291

1

3

333

6

3

33

2

22

1

11

−×=

⎥⎥⎦

⎤

⎢⎢⎣

⎡ ×+

×−+

×

×=

⎟⎟⎠

⎞⎜⎜⎝

⎛++=∑=

ALP

ALP

ALP

EEALP

i ii

iiδ

in.109.75 3−×=δ

Find the stresses and strains:(a) Change in length of the pipe(b) Lateral strain(c) Increase in outer and inner

diameters(d) Increase in wall thickness

(*tearing)

Normal stress (σ) : the subscript identifies the face on which the stress acts. Tension is positive and compression is negative.

Shear stress (τ) : it has two subscripts. The first subscript denotes the face on which the stress acts. The second subscript denotes the direction on that face.A shear stress is positive if it acts on a positive face and positive direction or if it acts in a negative face and negative direction.

xσ

xxσ

xyτ

From equilibrium principles:τxy = τyx , τxz = τzx , τzy = τyz

3D

TORSION(*twisting)

BENDING(*flexure)

IMc

M =σM

For 2-D:

yyxx maFmaF =Σ=Σ zzz IM α=ΣWhere αz is the angular acceleration

Moment of a Force about an axis

Free body Diagram

Change the steel for aluminum.

A steel strut S serving as a brace for a boat hoist transmits a compressive force P to the deck of a pier.

Bearing pad in shear. Elastomer with Modulus of Rigidity Ge

The connection shown in the figure consists of five steel plates, each 2.5mm thick, to be joined by a single bolt. Determine the required diameter of the bolt if the allowable bearing stress, σb, is 180.0MPa and the allowable shear stress, τallow, is 45.0MPa?

FBD

Determine the allowable load P based on the following four considerations.

Two-bar truss ABC supporting a sign of weight W. Determine the required cross-sectional area of bar AB and the required diameter of the pin at support C