Triangle Distributed Loading and Trigonometry Functions

Triangle distributed loading is a type of loading where the applied load varies linearly along the length of a structure, forming a triangular shape. This type of loading is commonly encountered in various engineering applications, such as beams, bridges, and cranes.

To determine the loading at any distance along the structure, trigonometry functions are used. Among the given options (a) Tangent, (b) Sine, (c) Cosine, and (d) Sine inverse, the correct trigonometry function to use is the tangent function.

Tangent Function
The tangent function, denoted as tan(x), relates the ratio of the length of the side opposite an angle to the length of the side adjacent to the angle in a right triangle. In the context of triangle distributed loading, the tangent function can be used to determine the loading at any distance along the structure.

Explanation
When a triangle distributed loading is applied to a structure, the load intensity varies linearly with distance. This means that the loading can be represented by a linear equation, such as y = mx + c, where y is the loading, x is the distance from a reference point, m is the slope of the loading, and c is the intercept with the y-axis.

The slope of the loading represents the rate at which the loading increases or decreases with distance. In the case of a triangle distributed loading, the slope is constant and corresponds to the rate of change of loading per unit distance.

To determine the loading at any distance x, the tangent function can be used to calculate the slope of the loading. The slope of the loading can be expressed as the ratio of the change in loading (Δy) to the change in distance (Δx) between two points on the loading curve.

The tangent function can be defined as tan(θ) = Δy/Δx, where θ is the angle of inclination of the loading curve.

By rearranging the equation, the change in loading (Δy) can be expressed as Δy = tan(θ) * Δx.

Therefore, the loading at any distance x can be found by multiplying the slope of the loading (tan(θ)) by the distance from the reference point (x), which gives the equation y = tan(θ) * x. This equation allows for the determination of the loading at any distance along the structure.

Conclusion
In triangle distributed loading, the loading at any distance can be easily found by using the tangent function. The tangent function relates the slope of the loading to the distance from a reference point. By multiplying the slope (tan(θ)) by the distance (x), the loading at any point can be determined.