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Visual Tips

SELFLEARNINGRAHUL

4 Aug, 2025

Chapter 3: Column Formulas (Visual Tips)

Chapter 3: Column Formulas (Visual Tips)

Short Columns

Short columns fail by **crushing**. Formula:

P = σ_allow × A

For concrete (f_ck=25 MPa), σ_allow ≈ 0.4 × f_ck.

Allowable Stress (σ in N/m²): Area (A in m²):

Eccentric Loads on Columns

Eccentric loads cause bending stress in addition to axial load:

σ = (P/A) ± (P × e × y) / I

Load (P in kN): Area (A in m²): Eccentricity (e in m): Distance (y in m): Moment of Inertia (I in m⁴):

Column Base Plate Design

Base plate distributes column load to foundation:

A_plate = P / σ_bearing

Load (P in kN): Bearing Stress (σ in N/m²):

Elastic Buckling

Euler’s formula applies for slender columns:

P_cr = (π² × E × I) / (K × L)²

Elastic Modulus (E in N/m²): Moment of Inertia (I in m⁴): Effective Length (L in m): K (Length Factor):

Ultimate Strength (Concrete Columns)

Limit State Design (IS 456):

P_u = 0.4f_ckA_c + 0.67f_yA_s

f_ck (MPa): A_c (m²): f_y (MPa): A_s (m²):

Steel Columns

ASD Design:

P = σ_allow × A

Allowable Stress (σ in N/m²): Area (A in m²):

SELFLEARNINGRAHUL

SELFLEARNINGRAHUL

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