Explanation :
a) To calculate the workload for the steel, we need to first convert the area of the steel from cm² to m².
Area of steel = 65 cm² = 65/10000 m² = 0.0065 m²
Now we can calculate the workload for the steel using the formula:
Workload = Stress x Area
Given that the working stress in the steel is 70 MPa, we convert it to Pa:
Stress = 70 MPa = 70 x 10^6 Pa
Workload = 70 x 10^6 Pa x 0.0065 m²
= 455,000 N
Therefore, the workload for the steel is 455,000 N.
b) To calculate the workload for the concrete, we subtract the area of the steel from the total area of the column.
Area of concrete = Total area - Area of steel
= 0.18650 m² - 0.0065 m²
= 0.18 m²
Now we can calculate the workload for the concrete using the formula:
Workload = Stress x Area
Given that the modulus of elasticity for the concrete is 13.8 GPa, we convert it to Pa:
Stress = 13.8 GPa = 13.8 x 10^9 Pa
Workload = 13.8 x 10^9 Pa x 0.180 m²
= 2,484,000,000 N
Therefore, the workload for the concrete is 2,484,000,000 N.
The total workload carried by the column is the sum of the workloads for the steel and concrete:
Total workload = Workload for steel + Workload for concrete
= 455,000 N + 2,484,000,000 N
= 2,484,455,000 N
Therefore, the total workload carried by the column is 2,484,455,000 N.
c) To calculate the shortening of the column, we can use Hooke's Law:
Shortening = Load / (Area x Modulus of elasticity)
Based on the information given, the area of the column is 0.18650 m² and the modulus of elasticity for the concrete is 13.8 GPa. We convert the modulus of elasticity to Pa:
Modulus of elasticity = 13.8 GPa = 13.8 x 10^9 Pa
Shortening = 2,484,455,000 N / (0.18650 m² x 13.8 x 10^9 Pa)
= 0.091 mm
Therefore, the shortening of the column when a workload is carried out on it is 0.091 mm.