Understanding Stress and Strain in Materials

The video tutorial covers the concepts of elastic modulus, compressive stress, and shear modulus. It begins with a problem involving a 300 kg block hanging on an aluminum rod, calculating the change in length using Young's modulus. The tutorial then shifts to a concrete column under compressive stress, determining the maximum force it can withstand. Finally, it examines the shear modulus by applying a horizontal force to an aluminum cube, calculating the resulting deformation. The video provides formulas and step-by-step calculations for each scenario, enhancing understanding of stress and strain in materials.

What is the formula to calculate the change in length of a rod using Young's modulus?

• Delta L = F * A / E

• Delta L = E * A / F

• Delta L = 1 / E * F / A * L0

• Delta L = E * F / A

How do you convert the change in length from meters to centimeters?

• Multiply by 100

• Divide by 10

• Divide by 100

• Multiply by 10

What is the tensile strain of a rod if the change in length is 4.278 x 10^-3 meters and the original length is 2 meters?

• 8.556 x 10^-3

• 4.278 x 10^-3

• 1.069 x 10^-3

• 2.139 x 10^-3

What is the tensile stress applied to the rod if the force is 300 kg * 9.8 m/s² and the area is pi * (0.0025 m)²?

• 149,732,270.5 N/m²

• 1,497,322.705 N/m²

• 14,973,227.05 N/m²

• 1,497,322,705 N/m²

Will the aluminum rod break if the tensile stress is 150 x 10^6 N/m² and the ultimate tensile strength is 200 x 10^6 N/m²?

• Yes, it will break

• No, it will not break

• It will bend but not break

• It will fracture slightly

What is the compressive stress on a concrete column with a 5000 kg block and a radius of 0.05 meters?

• 1.56 x 10^6 N/m²

• 12.48 x 10^6 N/m²

• 3.12 x 10^6 N/m²

• 6.24 x 10^6 N/m²

How can you calculate the compressive strain if the elastic modulus is known?

• Strain = Elastic Modulus * Stress

• Strain = Elastic Modulus / Stress

• Strain = Stress / Elastic Modulus

• Strain = Stress * Elastic Modulus

What is the maximum force a concrete column can support if its ultimate compressive strength is 20 x 10^6 N/m²?

• 157,080 N

• 1,570 N

• 1,570,800 N

• 15,708 N

How far will the top of an aluminum cube move if a shear force of 50,000 N is applied and the shear modulus is 25 x 10^9 N/m²?

• 0.002 mm

• 0.02 mm

• 0.2 mm

• 2 mm

What is the shear stress on an aluminum cube with a force of 50,000 N and an area of 0.01 m²?

• 500 x 10^6 N/m²

• 0.5 x 10^6 N/m²

• 50 x 10^6 N/m²

• 5 x 10^6 N/m²