Question

Problem 3: (15 points) A W12x65 is pinned at both ends and braced in the weak axis at the locations shown in the figure below. Use A992 steel for the column and determine the design compressive strength (.P.) using LRFD. Koti- Strong axis Weak axis

Answer 1

Given :

A = 19.1 in²

r_x = 5.28 in

r_y = 3.02 in

Fy = 50 ksi

Step 1 : Calculating Kl/r values on both the axis

Stronger axis (x axis)

Kl/r_x = (35×12)/5.28 = 79.54

Weak axis (y axis)

Column is braced in the weak axis, so column is divided in 3 parts

Kl/r_y is to be calculated for the 3 parts.

Part 1 and 3, Kl/r_y = (10×12)/3.02 = 39.73

Part 2, (15×12)/3.02 = 59.6

To calculate critical compression stress, largest kl/r governs

So, kl/r = 79.54 will be taken to find compressive strength

(Note. As column is braced in the weak axis, it no longer is weak because it's effective length decreases)

Step 2: Calculation of design compressive strength

Now, using table 4-22 of AISC 14th ed. Fy = 50 ksi.  

By interpolation, $\phi$ cFcr = 28.34 ksi

$\phi$_cPn = $\phi$ _cFcr x A = 28.34 × 19.1 = 541.29 k

Hence, design compressive strength of column is 541.29 k.