STRENGTHS
Chapter 9
9-1 Intro
• Dealing with relationship between the external loads
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applied to an elastic body and the intensity of the internal
forces acting within the body
Intensities of the internal resisting forces are called
stresses
Strengths deals with the deformations of the body
Deformation per unit length is called the strain
Subject of strength of materials involves strength – load
carrying capacity based on stresses inside a member,
stiffness deformation characteristics and stability the
ability of a slender member to maintain its initial
configuration without buckling while being subjected to
compressive loading
9-2 Normal and shear stresses
• Structural member is subjected to loads internal resisting
forces are generated within the member so that the
external forces can be balanced and the body can hold
itself together
• Intensities of internal forces per unit area are called
stresses
• Two types of stresses
• Norma tresses – perpendicular to the area
• Shear stresses by internal forces tangential to the area
• Us customary system – pounds per square inch (psi, psf,
or kips
• SI newtons per square meter (N/m²) also designated
pascal (Pa)
9-2 Normal and shear stresses
• 1 kPa = 10³ Pa
• 1 Mpa = 10(6) Pa
• 1 Gpa = 10(9) Pa
• Conversion factors
• 1 psi = 6.895 kPa
• 1 ksi = 6.895 Mpa
• 1 psf = 47.88 Pa
9-3 Direct Normal Stresses
• Bar uniform cross section is called a prismatic bar
• Subject to equal and opposite pulling forces
• A member subjected to axial loads is called an axially loaded
member
• Pulling forces to elongate stretch the bar = tension
• Pushing forces contract or shorten said to be in compression
• Uniform normal stress σ=p/a
• σ = normal stress in the cross section
• P = internal axial force at the section
• A = the cross sectional area of the rod
• Allowable axial load – members are limited stress level
called allowable stress σ allow – which is the upper limit
of stress not to be exceeded
9-3 Direct Normal Stresses
• Required Area = minimum cross section area A of a
member designed to carry a maximum axial load P
without exceeding the stress
• Internal Axial Force Diagram – variation of internal axial
force along the length of a member can be depicted by an
internal axial force diagram
• Tensile force are positive
• Compressive force as negative
• Example 9-1 page 326
• Example 9-2 page 326
• Example 9-3 page 328
• Example 9-4 page 329
9-4 Direct Shear Stresses
• Shear stress defined as intensity of internal force
tangential to the area in question
• Shear stress differs from normal stress because shear
stress is parallel to the area on which it acts while normal
stress is normal to the area
• Horizontal force P applied to the protruded part tends to
shear the part off the block along the shear plane abcd
• Body resists the force P by developing resisting shear stresses in
the shear plane
• Resultant of the shear stresses must be equal to the applied force
P
9-4 Direct Shear Stresses
• Ƭ(avg) = p/A
• Ƭ(avg) = the average shear stress
• P = the internal resisting shear force tangent to the shear plane
• A = the area of the shear plane
• Direct shear stresses are found in bolts , rivets, pins,
keys, etc.
• Lap joint
• Connecting two overlapping tension plates with a rivet – rivet is
subjected to shear stress through section m-m
• Shear stress in general is not uniformly distributed in the section
• Since shear stress occurs only in one section of the rivet it is called
a single shear
9-4 Direct Shear Stresses
• Butt Joint – connects non overlapping tension plates
using connecting plates
• Ƭ(avg) = P/2A
• Shear stresses occur in two sections of the rivet – rivet is said to be
in double shear
• Shaft Key –connects a gear to a shaft – moment M on the
gear is transmitted to the shaft through the key – the key
is subjected to forces
• P=M/r
• Average shear stress at section m-m of the key is Ƭ(avg)
=P/A=M/r/bL =M/rbL
• B is the width of the key , L is the length of the key, r is the radius of
the shaft
9-5 Bearing Stresses
• When one body presses against another bearing stress
occur between the two bodies
• Example 9-6 page 333
• Bearing stress in shaft key – occur between the key and
the gear between the key and shaft
• Example page 333
• Examples 9-5 page 334
• Examples 9-6 page 335
• Examples 9-7 page 336
• Examples 9-8 page 337
9-6 Stresses on Inclined Planes
• Both normal and shear stresses exist
• Force can be resolved into two components – normal
component perpendicular to the inclined plane and
tangential component parallel to the inclined plane
• The normal component produces normal stress and
tangential component produces shear stress
• Examples 9-9 page 339
• Example 9-10 page 340
9-7 Stresses in thin walled pressure
Vessels
• Are leak proof containers subjected to internal pressure ,
boilers, fire extinguishers and compressed air tanks are
examples
• Examples 9-11 page 343
• Examples 9-12 page 343
• Examples 9-13 page 344