You don't need the shear modulus to calculate the force. You can use the 2nd equation where pressure is the shear strength. And where A = ___??___Myung said:Homework Statement
How much force is required to punch a hole ½ in. in diameter from a 1/8 in. thick steel sheet of shearing strength 4x104 psi.
Homework Equations
Shearing Modulus = Pressure/Shearing Strain
Pressure = F/A
Shearing Strain = DistanceSheared/Length-to-be-sheared
The Attempt at a Solution
Can I first ask how can I use the Value of its Shearing Strength to the equation?
PhanthomJay said:You don't need the shear modulus to calculate the force. You can use the 2nd equation where pressure is the shear strength. And where A = ___??___
Myung said:A = ??
should I use the diameter or the thickness? or both? will that matter?
PhanthomJay said:Yes, it will matter; shear stresses act parallel to the cross section area, in the plane in which they act. Visualize the punch tearing through the entire thickness of metal. Intuitively, the thicker the metal, the greater will be the force required to punch through it. So the thickness is important in determining the Area. The area is the thickness times what other term?
Since the area of the hole is perpendicular to the applied force, it should not be included in the calculation of the area parallel to the applied force. So you just want the Area of the 'thickness', which is the thickness times the length of the thickness measured along the hole's circumference. That length is not 1/2 inch. When you get the answer for force, the units of force are in pounds, not Newtons.Myung said:A = the cross-sectional area of material with area parallel to the applied force vector.
A = Area of Hole(∏(1/2^2)/4) + Area of Thickness ( W = 1/8 , L = 1/2)
F = 10353.98 N?
Cross-sectional area is perpendicular to the Applied Force Vector while the Area of the Thickness is parallel to the said Vector.
Shearing Modulus/Shearing Strength is a measure of a material's resistance to shearing or cutting forces. It is a measure of how much deformation a material can withstand before it breaks or permanently deforms. It is also known as the shear modulus or shear stress.
Shearing Modulus/Shearing Strength is calculated by dividing the shear stress by the shear strain. The shear stress is the force applied to an object per unit area, while the shear strain is the amount of deformation per unit length. The resulting value is expressed in Pascals (Pa) or pounds per square inch (psi).
The main factors that affect Shearing Modulus/Shearing Strength are the type of material, its internal structure and composition, and the temperature and pressure at which it is subjected to. Additionally, the presence of defects or flaws in the material can also affect its shearing strength.
The main difference between Shearing Modulus and Shearing Strength is that the Shearing Modulus is a measure of a material's stiffness, while Shearing Strength is a measure of its resistance to shearing forces. Shearing Modulus is a constant value for a given material, while Shearing Strength can vary depending on the applied stress and the material's internal structure.
Shearing Modulus/Shearing Strength is used in engineering to design and analyze structures and materials that will be subjected to shearing forces. It is an important property to consider in the design of bridges, buildings, and other structures that need to withstand external loads. It is also used in the development of new materials with improved shearing properties.