材料力学(英文版)Chap1

材料力学(英文版)Chap1

Stress

A variable that can be used as a measure of strength of a structural member.Learning objectives

Understanding the concept of stress.

Understanding the two step analysis of relating stresses to external forces and moments.

Static

Equilibrium

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材料力学(英文版)Chap1

Normal Stress

TensileNormalForce

N

ImaginaryCut

TensileNormalStress

σavg

ChandelierWeight

ChandelierWeightBuildingWeight

BuildingWeight

ImaginaryCut

NNN

σavgσavgσavg

CompressiveNormalForce

CompressiveNormalStre

σav=N A

All internal forces (and moments) in the book are in bold italics Normal stress that pulls the surface away from the body is called a ten-sile stress.

Normal stress that pushes the surface into the body is called a com-pressive stress.

The normal stress acting in the direction of the axis of a slender mem-ber (rods, cables, bars, columns, etc.) is called the axial stress. The compressive normal stress that is produced when one surface presses against other is called the bearing stress.

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材料力学(英文版)Chap1

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材料力学(英文版)Chap1

Shear Stress

Imaginary cutbetween the walland the tape

WeightClothes

Imaginary cut

along the possible path of the edge of the ring.

Pullof thehand

V

WeightClothes

V

VV

Pullof thehand

τ

τ

Weightof theClothes

τ

ττ

Pullof thehand

(b)

(a)

τav=V A

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材料力学(英文版)Chap1

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材料力学(英文版)Chap1

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材料力学(英文版)Chap1

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材料力学(英文版)Chap1

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材料力学(英文版)Chap1

M. Vable

Mechanics of Materials: Chapter 1

Internally Distributed Force System(a) Normal to planeA

FB A B C D E B FC A C

A

FA FD

D E FE

Tangent in plane

(a)

(b)

The intensity of internal distributed forces on an imaginary cut surface of a body is called the stress on a surface. The intensity of internal distributed force that is normal to the surface of an imaginary cut is called the normal stress on a surface. The intensity of internal distributed force that is parallel to the surface of an imaginary cut surface is called the shear stress on the surface. Relating stresses to external forces and moments is a two step process.Static equivalency Equilibrium

Uniform Normal StressσavgPrinted from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

Uniform Shear Stressτavg

Normal stress x linear in y y z x y z Mz

Normal stress linear in z x y z x y z My

Uniform shear stre in tangen direction.

N=σ

avg

A

V=τ

avg

A

T

(a)

(b)

(c)

(d)

(e)

1-9

材料力学(英文版)Chap1

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材料力学(英文版)Chap1

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材料力学(英文版)Chap1

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材料力学(英文版)Chap1

Stress at a Point

OutwardnormalΔAi

ΔFj

InternalForce

ΔFj

σij=lim --------

ΔAi→0 ΔAi

directionoutwardnormaltotheimaginarycutsurface.

ofthe

internalforcecomponent.

ΔAi will be considered positive if the outward normal to the surface is in the positive i direction. A stress component is positive if numerator and denominator have the same sign. Thus σij is positive if: (1) ΔFj and ΔAi are both positive. (2) ΔFj and ΔAi are both negative.

σxx

Stress Matrix in 3-D: τyx

τzx

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τxyσyyτzy

τxzτyz . σzz

Table 1.1 Comparison of number of components

QuantityScalarVectorStress

One Dimension

1 = 101 = 111 = 12

Two Dimensions

1 = 202 = 214 = 22

Three Dimensions

1 = 30 3 = 31 9 = 32

材料力学(英文版)Chap1

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材料力学(英文版)Chap1

Construction of a Stress Element for Plane Stress:All stress components on a plane are zero

3-dimensional element

y

2-dimensional element

y

σyyC

τyx

τxydx

σxxτyx0

τxyσyy0

000

xx

yy

CB

yx

xy

dy

AD

dz

xx

x

σxx

Bdyτxy

yx

σyy

σxxdx

yy

Symmetric Shear Stresses: τxy=τyxτyz=τzyτzx=τxz A pair of symmetric shear stress points towards the corner or away from the corner.Stress cube showing all positive stress components

σxxτyxτzx

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τxyσyyτzy

τxzτyzσzz

材料力学(英文版)Chap1

of the cube.σxx=90MPa(C)τyx=–200MPa

τzx=0

τxy=–200MPaσyy=175MPa(C)τzy=225MPa

x.C

.B

.A

z

τxz=0τyz=225MPaσzz=150MPa(T)

Class Problem 4

Show the non-zero stress components of problem C1.6 on the A,B, and C faces of the cube below.

y

z

.C

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.B

x

.A

材料力学(英文版)Chap1

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