Dome Deflection Formula for Calculating Deflection from Point Load

In summary, Tadders is requesting for a formula to determine the deflection of a dome with known parameters, specifically the Poisson's ratio, spherical dome mean radius, spherical dome shell thickness, and subtended half angle. They also asked for the type of edge support, and provided the data for the material, including its Poisson's ratio, mean radius, shell thickness, subtended half angle, and edge support. Tadders also clarified that they are only interested in a point load deflection at the center of the dome on the convex side. They were also given a formula for the deflection in terms of the applied load and tensile modulus of elasticity, with specific conditions for its applicability.
  • #1
Tadders
3
0
I am looking for a formula to give me the deflection of a dome if all dome perameters are known from a point load at the center of the dome towards the dome on the convex side. I do not have the Roark book so I need the actual formula, not just a reference.
 
Engineering news on Phys.org
  • #2
Tadders: Can you provide numeric values for the following parameters, to narrow your question? Your question is currently slightly too generic to be easily answered.

nu = Poisson's ratio.
r = spherical dome mean radius.
t = spherical dome shell thickness.
phi = spherical dome subtended half angle, phi ≤ 90 deg, where phi = 90 deg is a hemispherical dome.
Also, type of edge support, if known (optional).
 
  • #3
nvn,
Here is the data:
Material 1070 steel
nu = 0.29
r = 22.08 inches
t = 4.5mm thick
phi = 21.24 degrees
edge support = free to rotate, there will be some lateral restraint for my application but for calc purposes say no restraint, and complete vertical restraint (vertical meaning in the direction of the central axis i.e. if the dome was a roof on a building, the edge could not move vertically).
 
  • #4
nvn,
PS to prior post. I am only interested in a point load deflection where the point load is at the center of the dome on the convex side towards the dome.
Thanks.
 
  • #5
Tadders: I assumed your point load is evenly distributed over a small circular area having a diameter of 4.5 mm. Therefore, the deflection at the center of the load is y = -10.942*P/E, where y = deflection (mm), P = total applied load (N), and E = tensile modulus of elasticity (MPa).

This answer is applicable only if r = 560.83 mm, t = 4.5 mm, nu = 0.29, and the diameter of the circular area of the applied load is 4.5 mm.
 
Last edited by a moderator:

What is the formula for calculating dome deflection?

The formula for calculating dome deflection is: D = (P*R^3)/(2*E*T), where D is the deflection, P is the pressure, R is the radius of the dome, E is the modulus of elasticity, and T is the thickness of the dome.

How do I determine the pressure to use in the formula?

The pressure used in the formula should be the maximum pressure that the dome will be subjected to. This can be determined based on the specific application and design of the dome.

What is the significance of the radius in the formula?

The radius of the dome is a crucial factor in the formula as it directly affects the amount of deflection that will occur. The larger the radius, the less deflection there will be.

What materials can be used for the modulus of elasticity in the formula?

The modulus of elasticity represents the stiffness of the material and can vary depending on the material used for the dome. Common materials used for domes include steel, concrete, and aluminum, each with their own modulus of elasticity values.

Are there any other factors that can affect dome deflection?

Yes, there are other factors that can affect dome deflection, such as wind and seismic loads, temperature changes, and construction tolerances. These should also be taken into consideration in the design and calculation of dome deflection.

Similar threads

Replies
6
Views
629
Replies
3
Views
2K
Replies
8
Views
4K
Replies
4
Views
2K
  • Mechanical Engineering
Replies
8
Views
951
  • Mechanical Engineering
Replies
2
Views
2K
Replies
33
Views
3K
  • Mechanical Engineering
Replies
5
Views
3K
  • Mechanical Engineering
Replies
2
Views
2K
  • Mechanical Engineering
Replies
6
Views
3K
Back
Top