*4-32. The A-36 steel column is encased in high-strengthconcrete as shown. If an axial force of 60 kip is appliedto the column, determine the required area of the steelso that the force is shared equally between the steel andconcrete. How far does the column shorten? It has anoriginal length of 8 ft.60 kipin.16 in.8 ft

Answered: *4-32. The A-36 steel column is encased…

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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*4-32. The A-36 steel column is encased in high-strength
concrete as shown. If an axial force of 60 kip is applied
to the column, determine the required area of the steel
so that the force is shared equally between the steel and
concrete. How far does the column shorten? It has an
original length of 8 ft.
60 kip
in.
16 in.
8 ft

Expert Solution

Step 1

$E_{s t} = 29 x 10^{3} k s i E_{c o n} = 4.2 x 10^{3} k s i 1 f t = 12 i n B a l a n c i n g a l l f o r c e s a l o n g v e r t i c a l d i r e c t i o n P_{s t} + P_{c o n} - 60 = 0 . . . (1) b u t i n t h e q u e s t i o n i t i s g i v e n t h a t P_{s t} = P_{c o n} S o, P_{s t} = P_{c o n} = P e q u a t i o n (1) b e c o m e s P + P - 60 = 0 2 P = 60 P = 30 k i p A s i t i s k n o w n t h a t [δ_{s t e e l} = δ_{c o n e}], s o δ = \frac{P L}{A_{c o n} . E_{c o n}} = \frac{P L}{A_{s t} E_{s t}} A_{s t} = \frac{A_{c o n} . E_{c o n}}{E_{s t}}$

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