Introduction to Engineering-Solid Mechanics 2.Stress and Strain Elongation and Strain The stretch or elongation 4L is one way to describe how the rod lengthens when F is applied If a second rod has the same cross-sectional area,but is shorter The stress within it would be the same as for the first rod The shorter rod would stretch by a smaller amount - Strain(a.is the amount of stretching per unit of length. △L = L Strain is a dimensionless quantity.Strain is generally very small. Introduction to Engineering 11 H.Shao
Introduction to Engineering Introduction to Engineering —— Solid Mechanics Solid Mechanics Introduction to Engineering Introduction to Engineering H. Shao 11 2. Stress and Strain Elongation and Strain – The stretch or elongation ΔL is one way to describe how the rod lengthens when F is applied – If a second rod has the same cross-sectional area, but is shorter • The stress within it would be the same as for the first rod • The shorter rod would stretch by a smaller amount – Strain (), is the amount of stretching per unit of length. – Strain is a dimensionless quantity. Strain is generally very small. L0 L
Introduction to Engineering-Solid Mechanics 2.Stress and Strain Application B 30° Tension Compression Introduction to Engineering 12 H.Shao
Introduction to Engineering Introduction to Engineering —— Solid Mechanics Solid Mechanics Introduction to Engineering Introduction to Engineering H. Shao 12 2. Stress and Strain Application Tension & Compression
Introduction to Engineering-Solid Mechanics 2.Stress and Strain Example The U-bolt is used to attach the body to its chassis.The U-bolt is made from a 10-mm-diameter rod,and the nuts on it are tightened until the tension is 4kN.Calculate the tensile stress in a straight section of the bolt. The cross-sectional area of the holt is d =78.5mm2=7.85×10-5m2 The stress becomes: F 4000W O= =5.1×10Pa=51MPa A 7.85×10-5m2 Introduction to Engineering 13 H.Shao
Introduction to Engineering Introduction to Engineering —— Solid Mechanics Solid Mechanics Introduction to Engineering Introduction to Engineering H. Shao 13 2. Stress and Strain Example The U-bolt is used to attach the body to its chassis. The U-bolt is made from a 10-mm-diameter rod, and the nuts on it are tightened until the tension is 4kN. Calculate the tensile stress in a straight section of the bolt. The cross-sectional area of the bolt is The stress becomes: 2 25 2 1085.75.78 4 mm m d A Pa MPa m N A F 51101.5 1085.7 4000 7 25
Introduction to Engineering-Solid Mechanics 3.Shear Suppose the force is perpendicular to the longitudinal axis.The stress will be a Shear Stress Shear stress occurs when something is being sliced or cut. ■ Shear stress is oriented in the same plane as the cross section, that is,in the direction parallel to the surface of the slice. ■ Tension is associated with a component that is being stretched or pulled apart. The two types of stress act in perpendicular direction. ■ The units for shear stress remain force-per-unit-area. Introduction to Engineering 14 H.Shao
Introduction to Engineering Introduction to Engineering —— Solid Mechanics Solid Mechanics Introduction to Engineering Introduction to Engineering H. Shao 14 3.Shear • Suppose the force is perpendicular to the longitudinal axis. The stress will be a Shear Stress • Shear stress occurs when something is being sliced or cut. Shear stress is oriented in the same plane as the cross section, that is, in the direction parallel to the surface of the slice. Tension is associated with a component that is being stretched or pulled apart. The two types of stress act in perpendicular direction. The units for shear stress remain force-per-unit-area. F
Introduction to Engineering-Solid Mechanics 3.Shear Shear Plane,Shear Force and Shear Stress Shear planes:As the force F is applied,along which the material tends to be sliced,sheared,or cut Shear forces:The two forces Vare oriented parallel to the shear planes. shear stress:r,is defined as T= A Shear plane Rigid Elastic block support 个个个个个个个个个个个 (a) Rigid support (b) (c) 个个个个个个个个个个个 Introduction to Engineering 15 H.Shao
Introduction to Engineering Introduction to Engineering —— Solid Mechanics Solid Mechanics Introduction to Engineering Introduction to Engineering H. Shao 15 3.Shear Shear Plane, Shear Force and Shear Stress Shear planes：As the force F is applied, along which the material tends to be sliced, sheared, or cut Shear forces: The two forces V are oriented parallel to the shear planes. shear stress: τ, is defined as F V V τ F Shear plane Rigid support Elastic block Rigid support (a) (b) (c) A V