Answer:
The Order is 4th order
Explanation:
Let take the diagram on the first uploaded image as an example of triangular distributed load
Let x denote the location
To obtain the vertical force acting at point a we integrate the function
[tex]\frac{dA_y}{dx} = w[/tex]
where [tex]A_y[/tex] is the vertical force
dx is the change in location
w is a single component of force acting downwards
[tex]A_y = \int\limits^L_0 {w} \, dx[/tex]
[tex]A_y = \int\limits^8_0 {\frac{x^2}{8} } \, dx[/tex]
= [tex]\frac{1}{8} [\frac{8^3}{3} ][/tex]
[tex]= 21.33N[/tex]
To obtain the moment of of inertia \
[tex]M_A = \int\limits^L_0 {wx} \, dx[/tex]
[tex]=\int\limits^8_0 {[\frac{x^2}{8} ]x} \, dx[/tex]
[tex]= \frac{8^4}{32}[/tex]
[tex]= 128 Nm[/tex]
To obtain the shear force acting at a distance x from A
[tex]V = A_y -\int\limits^x_0 {[\frac{x^2}{8} ]} \, dx[/tex]
[tex]= 21.33 - \frac{x^3}{24}[/tex]
To obtain the moment about the triangular distributed load section that is at a distance x from A as shown on the diagram
= > [tex]dM = \int\limits^x_0 {V} \, dx[/tex]
=> [tex]M_x -M_A = \int\limits^x_0 {[21.33- \frac{x^3}{24}]} \, dx[/tex]
=> [tex]M_x = 128 + 21.33x -\frac{x^4}{96}[/tex]
Looking at this equation as a polynomial we see that the order is 4 i.e [tex]x^4[/tex]
