Lecture Spring2015 01 Stress and Strain

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

mathematical expression

physical meaning

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

sin2θ=2 sinθ cosθ sin2θ = (1− cos2θ)/2 cos2θ= (1+ cos2θ)/2

−

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

substitute θ+90ο into θ:

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

= -20 =30

=40

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

Lecture Note by Shi-Yu Xu @ CityU, CA3687 : Soil Mechanics

Strains

J

„

„

„ „

The vertical component of the force F applied to the metal rod causes a vertical deformation of the rod, or axial strain, shown as vd in the diagram on the right. The horizontal component of F causes a horizontal skewing, or shear strain, shown by hd in the diagram on the right. The axial strain (or, normal strain) is measured as vd/L. The shear strain is measured as hd/L, which is equal to the tangent of angle J.

J J

Lecture Note108Shi-Yu Xu @ CityU, CA3687Shi Yu Mechanics CEE by Fall 2012 Lecture Note by : Soil Xu @ UCLA

By defination:

H{

Ldeformed  Lundeformed Lundeformed

Ÿ Ldeformed { 1  H  Lundeformed

„

State of strain of a material point in 2D: Hx , Hy , Jxy

State of strain of a material point in 3D: Hx , Hy , Hz , Jxy , Jyz , Jzx

„

Normal strains cause a change in volume of the element. Shear strains cause a change in the shape of the element. Normal strains are measured along the edges of the element, NOT measured in the Global x , y , and z directions. Shear strains are angles ! Small strain analysis: In most of the civil engineering problems, it is assumed...