材料力学(英文版)Chap1

Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

材料力学(英文版)Chap1

Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

材料力学(英文版)Chap1

Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

材料力学(英文版)Chap1

Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

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

Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

材料力学(英文版)Chap1

Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

材料力学(英文版)Chap1

Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

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

Printed from: http://www.me.mtu.edu/~mavable/MoM2nd.htm

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