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Shear Forces on Bolts

BoltedconnectioninasteelframeTheboltsmustwithstandtheshearforces

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Equilibrium analysis will determine the

force P, but not the strength or

the rigidity of the bar.

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Freebody diagram for determining the

internal force system acting on section

External forces acting on

a body.

Resolving the internal force

n o e ax a orce an

the shear force V.14062014 4StrengthofMaterialsI(Introduction)

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Deformations

produced

by

the

components

of

internal

forces

andcouples14062014 5StrengthofMaterialsI(Introduction)

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If the stress is uniformly distributed, we get

Otherwisewecallitaveragestress14062014 6StrengthofMaterialsI(Introduction)

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whenthe

loading

is

uniform,

its

resultant

passes roug ecen ro o e oa e area

Statics

(a)uniformlydistributedloadofintensityp(b)astaticallyequivalent centroidal forceP=pA14062014 7StrengthofMaterialsI(Introduction)

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Normalstressdistributionina

stripcaused

by

aconcentrated

load.

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Saint Venants Princi le

Thedifferencebetweentheeffectsoftwodifferentbutstaticallyequivalent

.

1. Most analysis in mechanics of materials is based on simplifications that can

be justified with Saint Venants principle.

2. We often replace loads (including support reactions) by their resultants

and ignore the effects of holes, grooves, and fillets on stresses and

deformations.

3. Many of the simplifications are not only justified but necessary.

4. Without simplifying assumptions, analysis would be exceedingly difficult.

5. However, we must always keep in mind the approximations that were

ma e, an ma e a owances or t em in t e ina esign.

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Normalstressdistributionina

groovedbar

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Stresses on Inclined Planes

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1. Maximum normal stress is P/A, and it acts on the cross

, .2. The shear stress is zero when = 0, as would be expected.3. The maximum shear stress is P/2A, which acts on the

planes inclined at = 45o to the cross section.

In summary, an axial load causes not only normal stress but also

s ear stress. T e magnitu es o ot stresses epen on t e

orientation of the plane on which they act.14062014 12StrengthofMaterialsI(Introduction)

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Stressesactingontwomutually

perpen cu ar

nc ne

sec onso

a

ar.

o,

stresses on a plane perpendicular to qplane

Stressesactingonmutuallyperpendicular,orcomplementaryplanes,theyarecalledcomplementarystresses.14062014 13StrengthofMaterialsI(Introduction)

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The shear stresses that act on complementary planes

ave e same magn u e u oppos e sense.

.

stress in the bar.

. .

3. The design criterion thus is that= P/A must not exceed the working stress

of the material from which the bar is to be fabricated.

4. The working stress, also called the allowable stress, is the largest value of

stress that can be safel carried b the material.

5. Working stress, denoted byw, will be discussed more fully later

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Procedure for Stress Analysis

n genera , e s ress ana ys s o an ax a y oa e mem er o a s ruc ureinvolves the following steps.

1. Equilibrium Analysis

If necessary, find the external reactions using a freebody diagram

(FBD) of the entire structure.

Compute the axial force P in the member using the method of sections.

This method introduces an imaginary cutting plane that isolates a

segment of the structure.

The cutting plane must include the cross section of the member of

interest.

The axial force acting in the member can then be found from the FBD of

FBD.14062014 15StrengthofMaterialsI(Introduction)

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1. Computation of Stress

1. After the axial force has been found b e uilibrium anal sis the

average normal stress in the member can be obtained from s=P/A,

plane.

. , =

far from applied loads and abrupt changes in the cross section (Saint

enant s pr nc p e .

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Design Considerations

For purposes of design, the computed stress

1. must be compared with the allowable stress, also called the working stress.

2. The working stress, which we denote by w, is discussed in detail in the next

chapter.3. To prevent failure of the member, the computed stress must be less than the

working stress.

. ote on t e na ys s o russes e usua assumpt ons ma e n t e ana ys s o

trusses are: (1) weights of the members are negligible compared to the applied

; v ; .

Under these assumptions, each member of the truss is an axially loaded bar.

.

method of joints (utilizing the freebody diagrams of the joints).

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Determinethenormalforce,shearforce,andmoment

atasection

through

point

C.

Take

P

=

8

kN.

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Thefloorcraneisusedtolifta600kgconcretepipe.Determinethe

.

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ExamplesSample

Problem

#1

The bar ABCD consists of three cylindrical steel segments with different lengths

and crosssectional areas. Axial loads are applied as shown. Calculate the normal

stress in each segment.

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Observe that the lengths of the segments do not affect the calculations of thestresses. Also, the fact that the bar is made of steel is irrelevant; the stresses in

the segments would be as calculated, regardless of the materials from which

the segments of the bar are fabricated.

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Forthetrussshownincalculatethenormalstressesin(1)member

AC;and(2)memberBD.Thecrosssectionalareaofeachmemberis

900mm2.

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The rectangular wood panel is formed by gluing together two boards along the

o .

carried safely by the panel if the working stress for the wood is 1120 psi, and the

respectively.

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Design for Working Stress in Wood

es gn or orma ress n ue

Design for Shear Stress in Glue

Maximum Load that can be carried

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