Roof Trusses The simplest type of roof truss is a triangle....

Roof Trusses The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If a 100 -pound force is applied at the peak of the truss, then the forces or weights $W_{1}$ and $W_{2}$ exerted parallel to each rafter of the truss are determined by the following linear system of equations. $$ \begin{array}{c} \frac{\sqrt{3}}{2}\left(W_{1}+W_{2}\right)=100 \\ W_{1}-W_{2}=0 \end{array} $$ Solve the system to find $W_{1}$ and $W_{2}$

Roof Trusses The simplest type of roof truss is a triangle. The truss shown in the figure is used to frame roofs of small buildings. If a 100 -pound force is applied at the peak of the truss, then the forces or weights $W_{1}$ and $W_{2}$ exerted parallel to each rafter of the truss are determined by the following linear system of equations.
$$ \begin{array}{c} \frac{\sqrt{3}}{2}\left(W_{1}+W_{2}\right)=100 \\ W_{1}-W_{2}=0 \end{array} $$
Solve the system to find $W_{1}$ and $W_{2}$

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Key Concepts

Force Decomposition Using Trigonometry

A technique that involves breaking a force into its component parts along specific directions using trigonometric ratios. This method is essential when dealing with forces applied at an angle, enabling one to analyze the effects of the force in different directions effectively.

Substitution Method in Algebra

An algebraic technique used to solve systems of equations by replacing one variable in one equation with an equivalent expression from another. This approach simplifies the system by reducing it to a single equation with one unknown, thereby facilitating the solution process.

Systems of Linear Equations

A set of linear equations involving the same variables, where the solution is the set of values that satisfies all equations simultaneously. In many applications, these systems model real-world phenomena where unknowns must be determined in relation to one another.

Equilibrium in Statics

A principle in mechanics stating that a system remains at rest when the sum of forces and moments acting on it are zero. This concept is crucial in analyzing structures to ensure that forces, such as tension or compression, are properly balanced.

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