Chapter 1 - Simple Stresses

 

 

C hapter 1

 

SIMPLE S TRESSES

1.1 INTRODU INTRODUCTI CTION ON

 Three fundamental areas of engineering mechanics 1. Sta Static ticss ooff Rig Rigid id Bodie Bodiess 2. Dyn Dynami amics cs ooff Rigi Rigidd Bo Bodie diess 3. Mec Mecha hanic nicss of Def Deform ormab able le Bo Bodie diess

Statics and Dynamics are devoted primarily to the study of external effects of force on rigid bodies. But in Strength of Materials deformations ho!ever small are of ma"or  interest. #he relations bet!een externally applied loads and their internal effects are studied here.   1-2 Analysis of Internal Forces

$ach compo $ach compone nent nt ref reflec lects ts a dif diffe feren rentt ef effe fect ct on the applied loads on the member and is given special name. Pxx (Axial/Normal Force)

Denoted as %. #his component measures the pulling or pushing action perpendicular to the section. (Pull) & #ensile force tends to elongate the member  (Push) & 'omp 'ompre ress ssiv ivee fo forc rcee te tend nd to sh shor orte tenn th thee member  

Figure1-1 Exploratory section a-a  through loaded member.

Pxy, Pxz (Shear Force) 

Denoted as (. #hese are components of the total resistance to sliding the portion to one side of the exploratory section past the other.

xx (!or"ue) 

Denoted as #. #his measures the resistance to t!isting the member.

xy, xz (#en$in% oments) Figure 1-2 Components of internal effects on exploratory section a-a



Denoted as M. #his measure the resistance to bending the member about ) or * axes. Chapter 1: Simple Stresses

 

  1-& SIP' S!SS  

 

measure of the strength of a material the capacity of the material in carrying the load By formula+ ,here+ - stress % - applied load   - cross§ional area

N*A' S!SS 

resisting area is perpendicular to the applied force

Fi%ure 1-& #ypes of /ormal Stress !ensile !e nsile stresses are

considered positive increase in length.

+omressie stresses are

In etric System.

 

-

considered negative producing a decrease in length

-

 N  mm 2

 - M%a

1 %ascal In n%lish System.

Chapter 1: Simple Stresses

 

   

-

lb ft 2 lb ¿2

 - psf   - psi

   

-

kips ft 2 kips ¿2

 - 0sf   - 0si

Chapter 1: Simple Stresses

 

Illustratie Prolems.

1.  hollo! steel tube !ith an inside diameter of 1 mm must carry a tensile load of   n. Determine the outside diameter of the tube if the stress is limited to 12 M/4m 2.

Solution+

% -  0/ -  /   - 12 M%a    

-

#hus   - 12 5  

6

D2 0  113&4 mm

 Chapter 1: Simple Stresses

 

2.  homogeneous 7&0g bar B is supported at either end by a cable as sho!n. 'alculate the smallest area of each cable if the stress is not to exceed 8 M%a in bron9e and 12 M%a in steel.

Solution+

3. #he :omogenous bar sho!n belo! is supported by a smooth pin at C and a cable that runs from A to B around the smooth peg at D. ;ind the stress in the cable if its diameter is .< in. and the bar m  

' >m

@ A# ?1@ ?sin 3.8.3 - 6 ?3.14@?. in. 2 determine the stress in each section.

Solution+

Exercise 1.1

 

NORMAL S TRESSES  Chapter 1: Simple Stresses

 

P*#'S.

1. n al alumi uminu num m rod is ri rigid gidly ly attach attached ed bet! bet!een een a stee steell rod and a br bron on9e 9e rod as sho!n in. xial loads are applied at the positions indicated. ;ind the maximum value of % that !ill not exceed a stress in steel of 1 M%a in aluminum of 8 M%a or in bron9e of 1 M%a.

  2. Dete Determin rminee the largest largest !eigh !eightt , that can be suppo supported rted by t!o !ires !ires sho!n. #he #he stress in either !ire is not to exceed 3 0si. #he cross§ional areas of !ires  B and ' are . in2 and .> in2 respectively.  

3.  12&i 12&in. n. suare ste steel el beari bearing ng plate lies bet! bet!een een an 7&in. dia diamete meterr !ooden !ooden post and a concrete footing as sho!n belo!. Determine the maximum value of the axial load % if the stress in !ood is limited to 17 psi and that in concrete to  psi.

83

;or the truss sho!n belo! calculate the stresses in members '$ D$ and D;. #he cross§ional area of each member is 1.7 in2. Cndicate tension ?#@ or compression ?'@.  Chapter 1: Simple Stresses

 

>. ;i ;ind nd the stres stresse sess in mem membe bers rs B' BD BD and and '; fo forr th thee tr trus usss sh sho! o!nn belo belo! !. Cndicate the tension or compression. #he cross§ional area of each member is 1. >.n n ?'ompre ?'ompression ssion@@

hp.WM' - 

ib.

h.3?4> BD@ - 3?. 2>.?1 ?1 @@ -

hr. BD - > 0/ ?# ?#eensio nsion@ n@

id.

hs.

ie.

ht.

if. ;or Membe Memberr B'+ B'+ ??see see ;BD 2 2@@

hu.> hu. > ?1@ hv.. hv

?1

# B

  RD - 1.13> # B

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#' - , H 2.22