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.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
Got questions? Join the online conversation and get instant answers!