Answered: A column is subjected to unfactored…

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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Question

A column is subjected to unfactored dead load = 200 kips and live load = 120 kips. Both ends of the column are fixed. The total length of the column is 18 ft in both the major and minor axes. If Fy = 50 ksi, choose the lightest W-shape that is adequate to take the loads per LRFD
method?

Expert Solution

Step 1: Factored design load

$\begin{array}{rcl} D L & = & D e a d l o a d = 200 k i p s \\ L L & = & L i v e l o a d = 120 k i p s \\ F a c t o r e d d e s i g n l o a d (P_{u}) & = & 1.2 D L + 1.6 L L \\ = & 1.2 \times 200 + 1.6 \times 120 \\ P_{u} & = & 432 k i p s \end{array}$

Step 2: Effective length of column

$L_{e f f} = K . L A s b o t h e n d s o f c o u l m n a r e f i x e d, K = 0.65, B e c a u s e c o l u m n i s u n b r a c e d, i t s l e n g t h i n b o t h x a n d y d i r e c t i o n w i l l b e s a m e, h e n c e, γ_{x} > γ_{y} f o r a l l W - s h a p e s, y - a x i s b u c k l i n g w i l l g o v e r n . K L_{y} = 0.65 \times 18 = 11.7 f t \approx 12 f t$

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