Deformation, stress, and strain problem.

In summary, a 24in diameter concrete column at the tenth story of an office building is supporting a flat roof slab under a wind uplift load of 50.00kips and a factored compressive force of 120.0kips. With a column length of 10.00ft and a concrete elasticity of 4200ksi, the area of the column is 452.39in^2. Using the equations for axial compressive and tensile stress, the net stress can be calculated to be 0.1547 ksi, with the type of stress dependent on whether the roof is carrying a compression or tension load. To determine the deformation and strain of the column, specific formulas for members under axial loads should
  • #1
vac
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Homework Statement


A 24in diameter concrete column, at tenth story of an office building, is supporting the flat roof slab is subjected to a wind uplift load of 50.00kips while carrying a factored
compressive force of 120.0kips. the column is 10.00ft long. Assume elasticity of concrete
to be 4200ksi and the ultimate compressive and ultimate tensile strength as 2.400kis and 0.2000ksi respectively. Determine:


Diameter: 24 in
Wind uplift load: 50 kips
Compressive force: 120 kips
Colums length: 10 ft
Concrete elasticity: 4200 ksi

Area (A): 452.39 in^2


Homework Equations


a) The axial compressive stress from compressive force only
b) The axial tensile stress from wind action only
c) The net stress
d) The deformation of the column
e) The strain in the column
f) The factor of safety? Is the column safe? Check whether the roof is carried away or not?


The Attempt at a Solution


A = 0.2653 ksi
B = 0.1105 ksi
C = 0.1547 ksi

Sorry, but I am not sure if my answers are correct.
Also I don't know how to solve d, e, and f.

Thanks in advance.
 
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  • #2
vac said:

Homework Statement


A 24in diameter concrete column, at tenth story of an office building, is supporting the flat roof slab is subjected to a wind uplift load of 50.00kips while carrying a factored
compressive force of 120.0kips. the column is 10.00ft long. Assume elasticity of concrete
to be 4200ksi and the ultimate compressive and ultimate tensile strength as 2.400kis and 0.2000ksi respectively. Determine:


Diameter: 24 in
Wind uplift load: 50 kips
Compressive force: 120 kips
Colums length: 10 ft
Concrete elasticity: 4200 ksi

Area (A): 452.39 in^2


Homework Equations


a) The axial compressive stress from compressive force only
b) The axial tensile stress from wind action only
c) The net stress
d) The deformation of the column
e) The strain in the column
f) The factor of safety? Is the column safe? Check whether the roof is carried away or not?


The Attempt at a Solution


A = 0.2653 ksi
B = 0.1105 ksi
C = 0.1547 ksi

Sorry, but I am not sure if my answers are correct.
Also I don't know how to solve d, e, and f.

Thanks in advance.
Your answers A and B look good, also C, but you should indicate for C whether net stress is compression or tension.

For deformation and strain, there are formulas you should look up for members under axial tensile or compressive loads.

For F, compare actual ultimate stresses to allowabale ultimate stresses to see if the column is safe.
 

1. What is deformation?

Deformation refers to the change in shape or size of a material caused by an external force. It can be temporary or permanent, depending on the material's elasticity.

2. What is the relationship between stress and strain?

Stress is the force applied to a material, while strain is the resulting change in shape or size. The relationship between stress and strain is described by Hooke's Law, which states that stress is directly proportional to strain, as long as the material remains within its elastic limit.

3. How is deformation measured?

Deformation can be measured using several methods, including strain gauges, extensometers, and optical methods. These tools measure the change in shape or size of a material and provide data on its deformation.

4. What factors affect the deformation of a material?

The deformation of a material is affected by several factors, including the type of material, its composition, temperature, and the magnitude and duration of the applied force. The material's elasticity and its ability to withstand stress also play a significant role in its deformation.

5. How is stress and strain analysis used in engineering?

Stress and strain analysis is used in engineering to predict and prevent failures in structures and materials. By understanding the stress and strain patterns, engineers can design and construct structures that can withstand expected loads and forces without deforming or breaking.

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