Question

A structure is designed using 4 circular columns. Due to a quirky design, the four columns will all carry different loads of 1800 N, 2100 N, 2275 N, and 2200 N. A factor of safety of 5 is used to design the columns. The diameter of each of the columns is supposed to be 50 cm, at most. Determine the maximum height of the structure (i.e. the column height) so that the structure will not fail. Assume that all columns may be modeled as Euler columns for your analysis. Assume a pinned-pinned boundary condition for your analysis, and assume the elastic modulus of the column material is 10 MPa.

Answer 1

Answer:

5.16 M

Explanation:

Loads ; 1800N, 2100N, 2275N, 2200N

safety factor = 5

diameter of each column = 50 cm = 0.5 m

Elastic modulus = 10 MPa

Calculate the max height of structure

moment of inertia for a circular section ( I ) = πd^4 / 64

lets represent the required maximum height of the column as L

Applying Euler column theory

The bucker load of the column =  ( attached below )

attached below is the remaining solution