Member of higher slenderness will collapse under a smaller compression load than a stocky member with the same cross sectional dimension. The more the height of the column the more the deflection and less the safe value of P. For this reason the P-∆ effect is a matter of study in long height column. The deflection and related additional secondary moment is significant and must be considered in design work. The deflection is proportional to the length of the column. Because the value of ∆ is for horizontal force H associated with end moments or Vice versa. Same phenomenon can be applied in P-∆ effect. And sometimes moment is calculated by multiplying the shear with the arm. In portal frame analysis the shear is calculated from moment divided by the arm. The final stage of Case 1 & Case 2 is same. In Figure (c) the combination of the two cases (a) + (b) is called P-∆ effect. In Figure (b) the member experienced a horizontal thrust / force which causes a significant value of deflection ∆. P-∆ concept Form Figure 2 it is seen that ∆ = column / member deflection In Figure (a) the value of ∆ is negligible for the applied P only.
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