Lengths of Frame Members

**redbullracer** · January 5th 2012, 10:06 AM

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.

$Lengths of Frame Members-untitled.png$

**skeeter** · January 5th 2012, 10:34 AM

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 ...

**Soroban** · January 5th 2012, 11:31 AM

Hello, redbullracer!

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

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

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

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

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

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

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

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

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Re: Little brain teaser :P

Re: Little brain teaser :P

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