# 1.5 Example with different effective lengths

 Page 1 / 1

#### Problem

A W12 X 65 column, 24 feet long, is pinned at both ends in the strong direction, and pinned at the midpoint and theends in the weak direction. The column has A36 steel.

#### Number 1 - find effective length

Since the x-direction is the strong one and the y-direction is the weak one, then:

${L}_{x}=24$
${L}_{y}=12$

Notice that the effective length in the y-direction is half the total length of the member because there is alateral support at the midpoint.

Looking at the Manual on page 16.1-189 shows that the $K$ value for a column pinned at both ends is 1.0. Since the column is pinned at the ends and at the middle,

${K}_{x}=1$
${K}_{y}=1$

Now we can say that:

${K}_{x}{L}_{x}=1\times 24=24$
${K}_{y}{L}_{y}=1\times 12=12$

#### Number 2 - finding the capacity

Since, the steel is A36, you cannot use the column tables from Chapter 4 of the Third Edition Manual as the values are all given in terms of ${F}_{y}=50\mathrm{ksi}$ . However, in the Second Edition, in Chapter 3, the column tables give information forterms of ${F}_{y}=36\mathrm{ksi}$ .

From page 3-24 of the Second Edition Manual , the capacity for a W12 X 65 column with ${K}_{y}{L}_{y}=12$ is 519 kips.

Then to find ${K}_{x}{L}_{x}$ in terms of ${r}_{y}$ , ${K}_{x}{L}_{x}$ must be divided by: $\frac{{r}_{x}}{{r}_{y}}$ . This gives:

$\frac{{K}_{x}{L}_{x}}{\frac{{r}_{x}}{{r}_{y}}}=\frac{24}{1.75}=13.71$

This is close enough to 14, that we can then look in the tables for the $\mathrm{KL}$ value of 14, or interpolate for 13.71) and find the capacity forthe W12 X 65 member. The capacity is 497kips.

#### Method 2 - with buckling formulas

If you do not have the tables for A36 steel, you must use the formulas on page 16.1-27 of the Manual .

#### Number 1 - show the width-thickness ratio

In order for the equations in section E2 of the Manual to apply, the width-thickness ratio must be ${\lambda }_{r}$ .

$\frac{{b}_{f}}{2{t}_{f}}< {\lambda }_{r}$

The value for $\frac{{b}_{f}}{2{t}_{f}}$ (9.92) can be found on page 16.1-21, as well as the value for $\frac{h}{{t}_{w}}$ (24.9). The formula for ${\lambda }_{r}$ can be found on page 16.1-14/15. Then, the value for that formula can be found on page 16.1-150.

The flanges are unstiffened and in pure compression, so the formula is:

$\frac{{b}_{f}}{2{t}_{f}}=9.92< 0.56\sqrt{\frac{E}{{F}_{y}}}=15.9$

The web is stiffened and in compression, so the formula is:

$\frac{h}{{t}_{w}}=24.9\le 1.49\sqrt{\frac{E}{{F}_{y}}}=42.3$

Another way to easily find the formulas for ${\lambda }_{r}$ is to go to page 16.1-183 and look at the picture of the I-shaped member. The arrows point to either the flange orthe web and formulas correspond to the arrows giving the axial compression formulas that you need for that elementof the member.

#### Number 2 - compute slenderness ratios

The slenderness ratios can be found for both the x-axis and the y-axis. We know $K$ , and $L$ , and $r$ can be found in the properties section of the Manual on page 1-20.

$\frac{{K}_{x}{L}_{x}}{{r}_{x}}=\frac{24\times 12\times 1}{5.28}=54.54$
$\frac{{K}_{y}{L}_{y}}{{r}_{x}}=\frac{12\times 12\times 1}{3.02}=47.68$

Then, using Table 3-36 on page 16.1-143 of the Manual and interpolation, we can determine that ${\phi }_{c}{F}_{cr}=26.21$ , and that ${\phi }_{c}{P}_{n}={\phi }_{c}{F}_{cr}{A}_{g}=500k$

The capacity of the W12 X 65 column is 500 kips.

can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
is it 3×y ?
J, combine like terms 7x-4y
im not good at math so would this help me
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!