# Lengths of Frame Members

• Jan 5th 2012, 10:06 AM
redbullracer
Lengths of Frame Members
You work in the design department of a company which produces fabricated steel structures and have been given sketches of two frames. For each, work out the lengths of all the members and the angles involved. The roof frame shown below is symmetrical about a centre line axis.

Attachment 23187
• Jan 5th 2012, 10:34 AM
skeeter
Re: Little brain teaser :P
Quote:

You work in the design department of a company which produces fabricated steel structures and have been given sketches of two frames. For each, work out the lengths of all the members and the angles involved. The roof frame shown below is symmetrical about a centre line axis.
so that those interested may see the diagram ...

http://www.mathhelpforum.com/math-he...p-untitled.png
• Jan 5th 2012, 11:31 AM
Soroban
Re: Little brain teaser :P
Hello, redbullracer!

Quote:

You work in the design department of a company which produces
fabricated steel structures and have been given sketches of two frames.
For each, work out the lengths of all the members and the angles involved.
The roof frame shown below is symmetrical about a centre line axis.

Code:

                  B                   o                 **:**               * * : * *             *20*  :  *  *         6 *  * 5 :  *  *         *    *    :    *    *     A o  *  o  *  o  *  o  *  o C             D    F    E

In $\displaystyle \Delta ABD$, Law of Cosines: .$\displaystyle AD^2 \:=\:5^2 + 6^2 - 2(5)(6)\cos20^o \:=\:4.618442753$

. . Hence: .$\displaystyle AD \:=\:2.149056247 \quad\Rightarrow\quad \boxed{AD \:\approx\:2.15}$

Then: .$\displaystyle \cos A \:=\:\frac{6^2 + 2.15^2 - 5^2}{2(6)(2.15)} \:=\:0.605523256$

. . Hence: .$\displaystyle A \:=\:52.73349563^o \quad\Rightarrow\quad \boxed{A \:\approx\: 52.73^o}$

Then: .$\displaystyle \angle ABF \:=\:90^o - 52.73^o \:=\:37.27^o$

. . Hence: .$\displaystyle \angle DBF \:=\:37.27^o - 20^o \quad\Rightarrow\qyad \boxed{\angle DBF \:=\:17.27^o}$

Then in $\displaystyle \Delta DBF:\,DF \,=\,5\sin12.27^o \:=\:1.484374609 \quad\Rightarrow\quad \boxed{DF \:\approx\:1.48}$

. . and: .$\displaystyle \angle BDF \:=\:90^o - 12.27^o \quad\Rightarrow\quad \boxed{\angle BDF \:=\:77.73^o }$

• Oct 30th 2017, 08:10 AM
davefrick1
Re: Lengths of Frame Members
what is the length of d to e in this question??
• Oct 30th 2017, 08:32 AM
skeeter
Re: Lengths of Frame Members
Quote:

Originally Posted by davefrick1
what is the length of d to e in this question??

two times the length of DF