Determine the length of member AB of the truss


Determine the length of member AB of the truss by first establishing a Cartesian position vector from A to B and then determining its magnitude.

Determine the length of member AB of the truss

Image from: Hibbeler, R. C., S. C. Fan, Kai Beng. Yap, and Peter Schiavone. Statics: Mechanics for Engineers. Singapore: Pearson, 2013.

Solution:

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Let’s first figure out where point A and B is with respect to the origin (0i+0j+0k).

Determine the length of member AB of the truss

Let’s write the location of point A in Cartesian vector notation.

A:(0.8i+1.2j) m

To find point B, we will have to use trigonometry.

Determine the length of member AB of the truss

We need to figure out the length of a so that we can figure out the total x-axis length of point B. To do so, we can write an equation using the tangent function.

\tan40^0\,=\,\dfrac{1.5}{a}

a\,=\,1.79 m

Therefore, the total x-length of point B is 0.8 + 0.3 + 1.79 = 2.89 m.

Let us now write point B in Cartesian vector notation.

B:(2.89i+1.5j) m

 

We can now find the position vector r_{AB} by subtracting the corresponding coordinates of A from B.

r_{AB}\,=\,\left\{(2.89-0.8)i+(1.5-1.2)j\right\} m

r_{AB}\,=\,\left\{(2.09)i+(0.3)j\right\}

 

We can now figure out the length of member AB by finding the magnitude of r_{AB}.

magnitude of r_{AB}\,=\,\sqrt{(2.09^2)+(0.3)^2}\,=\,2.11 m

 

Final Answer:

The length of member AB = 2.11 m

 

See more examples similar to this question like finding the lengths of wires using the same method.

This question can be found in Engineering Mechanics: Statics (SI edition), 13th edition, chapter 2, question 2-88.

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