A rectangular steel bar 14mm x 20mm x 250mm long extend by 0.15mm and subjected to a stress of 270N/mm^2.
1) calculate the tensile force of the rectangular steel bar
2) calculate strain of the steel bar
3) calculate modulus of elasticity of the steel bar
1) To calculate the tensile force of the rectangular steel bar, we can use the formula:
Tensile Force = Stress x Cross-sectional Area
First, we need to calculate the cross-sectional area of the steel bar. The cross-sectional area of a rectangular shape is given by the formula:
Area = Length x Width
Area = 14mm x 20mm = 280mm^2
Now we can calculate the tensile force:
Tensile Force = 270N/mm^2 x 280mm^2
Tensile Force = 75,600 N
Therefore, the tensile force of the rectangular steel bar is 75,600 N.
2) To calculate the strain of the steel bar, we can use the formula:
Strain = Change in Length / Original Length
Given that the steel bar extends by 0.15mm and the original length is 250mm, we can plug in these values:
Strain = 0.15mm / 250mm
Strain = 0.0006
Therefore, the strain of the steel bar is 0.0006.
3) To calculate the modulus of elasticity of the steel bar, we can use the formula:
Modulus of Elasticity = Stress / Strain
Given that the stress is 270N/mm^2 and the strain is 0.0006, we can plug in these values:
Modulus of Elasticity = 270N/mm^2 / 0.0006
Modulus of Elasticity = 450,000 N/mm^2
Therefore, the modulus of elasticity of the steel bar is 450,000 N/mm^2.
To solve these calculations, we need to use the formulas related to stress, strain, and the modulus of elasticity.
1) To calculate the tensile force of the rectangular steel bar, we will use the formula:
Tensile force = Stress x Cross-sectional area
Given that the rectangular steel bar has dimensions of 14mm x 20mm and is subjected to a stress of 270 N/mm^2, we can calculate the cross-sectional area as follows:
Cross-sectional area = length x width
Cross-sectional area = 14mm x 20mm
Cross-sectional area = 280 mm^2
Now, we can calculate the tensile force:
Tensile force = 270 N/mm^2 x 280 mm^2
Tensile force = 75,600 N
Therefore, the tensile force of the rectangular steel bar is 75,600 N.
2) To calculate the strain of the steel bar, we will use the formula:
Strain = Change in length / Original length
Given that the steel bar extends by 0.15 mm and the original length of the bar is 250 mm, we can calculate the strain as follows:
Strain = 0.15 mm / 250 mm
Strain = 0.0006
Therefore, the strain of the steel bar is 0.0006.
3) To calculate the modulus of elasticity of the steel bar, we will use the formula:
Modulus of elasticity = Stress / Strain
Given that the stress is 270 N/mm^2 and the strain is 0.0006, we can calculate the modulus of elasticity as follows:
Modulus of elasticity = 270 N/mm^2 / 0.0006
Modulus of elasticity = 450,000 N/mm^2
Therefore, the modulus of elasticity of the steel bar is 450,000 N/mm^2.