HP 50g Graphing, 48gII Graphing manual Elastic Buckling 1, Eccentric Columns 1, Equations, Example

Elastic Buckling (1, 1)

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

Equations:

Pcr = π2 ⋅ E ⋅ A K ⋅ L 2  r 

Pcr =	π2 ⋅ E ⋅ I		σ cr =	Pcr	r =	I
	(K ⋅ L)	2		A		A

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:



σmax = P ⋅ 1 +∈⋅ c A  r2







⋅ 

COS

1

K ⋅ L ⋅

 2 ⋅ r

	 
	 	r =	I
	 
P			A
	 
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.

54 Equation Reference