Steel column is 80 feet tall.
Column is a W 14 x 730(wide-flange beam)
The cross sectional area is 215 sq in.
Supports a floor load of 6600 K.
Determine the stress in the column and how much it will shorten due to the 6600K load.
(Assume E= 29,000,000 lb/sq in)
To determine the stress in the column and how much it will shorten due to the load, we can follow these steps:
Step 1: Calculate the load per unit area:
The load is given as 6600 K (Kips), which is 6600,000 pounds. The cross-sectional area of the column is given as 215 square inches. Therefore, the load per unit area (stress) can be calculated as:
Stress = Load / Area
Stress = 6600,000 lb / 215 sq in
Step 2: Calculate the stress in pounds per square inch (psi):
To get the stress in pounds per square inch (psi), divide the stress calculated in step 1 by the cross-sectional area in square inches:
Stress (psi) = Stress (lb/in²) / 1 in²
Step 3: Calculate the column elongation (shortening):
The elongation (ΔL) of the column can be calculated using Hooke's Law, which states that the elongation of an object is proportional to the applied stress and its material's modulus of elasticity (E). The formula to calculate the elongation is:
ΔL = (Load * Length) / (Area * E)
Step 4: Plug in the values to calculate the stress and elongation:
- Length (L) = 80 feet = 960 inches
- Modulus of Elasticity (E) = 29,000,000 lb/in²
Using the values from step 2 and 3, calculate the stress in psi and elongation of the column in inches.
Let's calculate them step by step:
Step 1: Calculate the load per unit area:
Stress = Load / Area
Stress = 6600,000 lb / 215 sq in
Step 2: Calculate the stress in pounds per square inch (psi):
Stress (psi) = Stress (lb/in²) / 1 in²
Step 3: Calculate the column elongation (shortening):
ΔL = (Load * Length) / (Area * E)
Step 4: Plug in the values to calculate the stress and elongation:
- Length (L) = 80 feet = 960 inches
- Modulus of Elasticity (E) = 29,000,000 lb/in²
Plug in the values and evaluate the equations to find the stress and elongation.