Lecture 01

 

STRENGTH OF MATERIALS-I Engr Mehwish Asad Assistant Professor 

 

Introduction ourse I!" E-#$% redit Hours" #&' ( ) S*ecific O+,ecties of ourse" 



To enable students to learn fundamentals fundamentals   regarding strength of materials. materials. To enhance skills of utilizing   materials of appropriate strength  strength  for civil engineering application.

 

Introduction At the end of this course, students will be able to: No CLO Statement PLO iscuss materials and their ulizaon in considering engineering PLO-1 CLO-1 structures properes analyze   A""l#  fundamental concepts to analyze A""l# design structural  structural members CLO-! and design PLO-2 subjected to various loadings CLO-$

 safety  analysis analysis of  of structural Perform members

PLO-2

Bloom’s C-2

C-3 C-3

 

Reference +oo.s

1.Beer, F. P., E. R. Johnston, J. T. e!olf, and . F. "a#urek $%&11' Mechanics of Materials, Materials, 6 th  Edition,, "c(ra) *ill. Edition %.*ibbeler, R. +. $%&11' Mechanics of Materials, Materials, 8th Edition, Edition, Prentice *all. .(ere, J. "., and B. J. (oodno $%&1%' Mechanics of Materials, Materials, Brief edition, +enage -earning. .P/tel, 0., F. -. inger $1234' Strength of Materials,, 4th Edition Materials Edition,, *arper 5nternationa 5nternational. l.

 

ourse ontents Si/*0e stress and strain T/pes of stresses and strains, taticall/ determinate and indeterminate compatibilit/ problems, +ompound bars, Temperatur emperature e stresses. Ana01sis of 2ea/s  0dvanced  0dvance d cases of shearing forces and bending moment diagrams for determinate beams, Relationship bet)een loads, shear force and bending moment, Theor/ of simple bending, istribution of shear stresses in beams of s/mmetrical sections. Principle of superposition, eflection of beams using double integration, moment area and con6ugate beam methods. ircu0ar Shafts" Torsion Shafts" Torsion of hollo) and solid circular section.

 

ourse ontents o0u/n and Struts +olumns, T/pes and different formulae for critical load like Euler7s formula, and Empirical formula like Rankine (ordon Formula, initiall/ imperfect columns, slenderness ratio. Strain Energ1"  Energ1"  train energ/ due to direct load, shear bending and torsion, 5mpact loads. S*rings" 8pen S*rings"  8pen coil springs, closed coil springs, leaf springs. Introduction to Torsion of Thin 3a00ed Tu+es and Nonircu0ar Me/+ers Thin4 Thic. and o/*ound 10inders Fatigue" Fatigue due to c/clic loading, iscontinuities and tress Fatigue" Fatigue +oncentration, +orrosion Fatigue, -o) +/clic Fatigue and 9:;

 

Lecture $'

 

Lecture ontents This lecture covers  efinition of trength of materials  Revision of basics

+onsider a bod/ as sho)n. 5t is held in e@uilibrium b/ e=ternal applied forces.

 

Ana01sis of Interna0 Forces >

-et us cut a section and consider one part to e=plore the internal forces.

 

Ana01sis of Interna0 Forces >

 0lthough the e=act distribution of this internal loading ma/ be unkno)n, use e@uations of e@uilibrium to relate e=ternal forces on bottom part of the bod/ to the resultant force and moment, and at an/ specific point 8 on the

sectioned area  

Ana01sis of Interna0 Forces >

Establish =, / and # a=is at origin 8 and split the resultant into respective components.

 

Ana01sis of Interna0 Forces C=, C/

hear Force

;#

;ormal Force

"=, "/

Bending "oment

T#

Torsion

Note"  If a body is s!b&e$ted to $oplanar syste" Note"  of for$es' only nor"al for$e shear for$e and bendin "o"ent #ill eist at a se$tion%

 

Ana01sis of Interna0 Forces Nor/a0 force4 N7 This force acts perpendicular to the area. 5t is developed )henever the e=ternal loads tend to push or pull on the t)o segments of the bod/. Shear force4 87 The shear force lies in the plane of the area and it is developed )hen the e=ternal loads tend to cause the t)o segments of the bod/ to slide over one another.

 

Ana01sis of Interna0 Forces Torsiona0 /o/ent or tor5ue4 T7 This effect is developed )hen the e=ternal loads tend to t)ist one segment of the bod/ )ith respect to the other about an a=is perpendicular to the area. 2ending /o/ent4 M7 The bending moment is caused b/ the e=ternal loads that tend to bend the bod/ about an a=is l/ing )ithin the plane of the area.

 

Ana01sis of Interna0 Forces 5f a bod/ is sub6ected to coplanar s/stem of forces? onl/ normal force, shear force and bending moment )ill e=ist at a section.

 

Chapter-1

S%&'SS What comes to our mind !hen ou heard this !ord "#$%&##'

 

STRESS

 

STRESS

>

tress is defined as the intensit/ of a force O* 

>

Force acting per unit area is kno)n as tress.

 

STRESS

3hat is Strength9

 

STRESS

3hat is the difference +etween Stress and Strength9

 

A(ial Loadin)

What do you underst understand and by Axial Loading??? 

 

STRESS >

A6ia0 Loading: Nor/a0 Stress"  Stress"  Force per unit area acting perpendicular to section under observation is kno)n as ;ormal tress. OR

>

;ormal force per unit area is ;ormal tress.

 

STRESS

 

E;AMPLE"

STRESS a'

free:bod/ diagram of a segment of the bar,

b'

segment of the before loading,

bar

c'

segment of the after loading, and

bar

d'

normal stresses in the bar 

 

STRESS E6a/*0e" > 5f t)o

bars

of

same

length and different cross:sectional areas are sub6ected to different loading, load carr/ing capacit/ of a bar cannot be 6ustified b/ the amount carried b/of an/load bar. being

 

STRESS >

5f )e see the dispersion of load on respective cross:sections )e )ill find a common factor of comparison for )hich bar is stronger than the other. This common factor is tress denoted b/ D.

>

!here P is the applied load and 0 is the cross:sectional area

 

STRESS >

>

This e@uation can give us the average stress and not the stress at all points )hich can be determined b/ differential load over differential area. There are certain conditions under )hich the stress is uniform across the entire section.

 

STRESS > > > >

+onsider the sho)n. tress is not

section uniform

across the section. tress concentrations can be clearl/ seen. The conditions under )hich stress is uniform occurs at section f:f and b:b.

 

STRESS These conditions are illustrated belo)? 1. The section !ood 6oint sho)n in fig belo) is an e=ample of single shear and the connection is referred to as lap 6oint.

 

STRESS !ou+0e Shear" > !ood 6oint sho)n in fig belo) is an e=ample of double shear and the connection is referred to as double lap  6oint.

 

Bearin) Stress

What doBearing???  you underst understand and by

 

STRESS

 

STRESS >

2earing Stress" is a normal stress that is produced b/ the compression of one surface against

>

another surface. E=ample for bearing stress is

soil pressure under piers.  

STRESS >

 0nother e=ample for bearing stress is stress developed at bolt connection.

 

STRESS Pro+0e/ State/ent"  State/ent"  The t)o members are pinned at B as sho)n in Fig. top vie)s of the pin connections at 0 have and Banare also given in the figure. 5f the pins allo)able shear stress of G1%.Iksi and the allo)able tensile stress of rod +B is G1H.%ksi, determine to the nearest 1 The first step is to calculate the reaction at supports.

 

STRESS >

ince Pin at 0 is sub6ected to double shear and that at B is sub6ected to single shear.

 

STRESS >

ince

 

STRESS >

>

o )e can select the bolt si#e nearest to 1