Answered: 10 in. P 18 ft

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

The W14 * 53 structural A992 steel column is ixed at its base and free at its top. If P = 75 kip, determine the sidesway delection at its top and the maximum stress in the column.

Expert Solution

Step 1

The properties of $W 14 \times 53 A 992$ steel column are,

The area of the column cross section is $A = 15.6 {in}^{2}$ .

The moment of inertia of the cross section about x axis is $I_{x} = 541 {in}^{4}$ .

The moment of inertia of the cross section about y axis is $I_{y} = 57.7 {in}^{4}$ .

The radius of gyration with respect to the x axis is $r_{x} = 5.89 in$ .

The depth of column cross section is $13.92 in$ .

The eccentricity is $e = 10 in$

The distance between the centroidal axis and the outer layer of the cross section of the column is,

$\begin{array}{rcl} c & = & \frac{d}{2} \\ = & \frac{13.92}{2} in \end{array}$

Step 2

The expression for deflection is given by,

$v_{m a x} = e [s e c (\sqrt{\frac{P}{E I_{x}}} \frac{K L}{2}) - 1]$

Here, $v_{m a x}$ is the maximum deflection, P is the eccentric load acting on the column and E is the young's modulus for steel material.

Substitute the values in the above expression.

$\begin{array}{rcl} v_{m a x} & = & (10) [s e c ((\sqrt{\frac{75}{29 \times 10^{4} \times 54}}) \frac{2 (18 ft \times \frac{12 in}{1 ft})}{2}) - 1] \\ = & 10 [s e c (0.4772267) - 1] \\ = & 1.23 in \end{array}$

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.

Similar questions