Elastic Buckling (1, 1)

These equations apply to a slender column (K — L / r > 100) with length factor K.

Equations:

Pcr =

π2

⋅ E ⋅ A

Pcr =

π2

⋅ E ⋅ I

σ cr =

Pcr

I

----------------------K⋅ L2

--------------------(K⋅ L)2

--------A

r = ---

 

 

 

A

 

-----------

 

 

 

 

 

 

 

r

 

 

 

 

 

 

Example:

Given: L=7.3152_m, r=4.1148_cm, E=199947961.502_kPa, A=53.0967_cm^2, K=0.7, I=8990598.7930_mm^4.

Solution: Pcr=676.6019_kN, σcr=127428.2444_kPa.

Eccentric Columns (1, 2)

These equations apply to a slender column (K — L / r > 100) with length factor K.

Equations:

 

 

 

 

 

 

 



 

σ max =

P

1 +

∈⋅ c

1

 

 



I

A---

⋅ 

---------r2

⋅ ----------------------------------------------------

 

 

-

r = ---

 

 

K ⋅ L

⋅

P



A

 

 

 

 

COS

-----------2⋅ r

E-----------⋅A 

 

Example:

Given: L=6.6542_m, A=187.9351_cm^2, r=8.4836_cm, E=206842718.795_kPa, I=135259652.16_mm^4, K=1,

P=1908.2571_kN, c=15.24_cm, ∈ =1.1806_cm.

Solution: σmax=140853.0970_kPa.

5-4 Equation Reference