Statics/Moments - Force perpendicular to slope?

[AndrewZzz]

Determine the resultant moment at support points A and B due to the forces acting on the truss as shown.




Fx = F(cos∅), Fy = F(sin∅), M = F(distance)



Point A -88.98kN*m
Point B ?

I have no problem calculating most of the forces, but I'm lost when it comes to knowing what to do with the forces that are perpendicular to the sloped surfaces. Do I calculate X and Y components for them? Does it automatically turn into an X or Y component? When trying to calculate the moment on point B, is the 10kN multiplied by zero because it's on the same x-axis as the point, or is the 10kN a Y component? Some insight would be hugely appreciated.

 

[bschwartz]

Yes, for any forces that are at an angle, generate the x and y components of the force. And good catch, the 10kN force will be multiplied by zero because it is on the same x-axis as point B (when calculating the reaction at B). However, only the x-component of that force is neglected in the calculations, be sure to include the y-component.

 

[AndrewZzz]

I figured it would still require the X and Y components! Which angle would I use to calculate those?

 

[bschwartz]

The angle should be 45degrees so the x-component is 10cos(45) and the y-component is 10sin(45). At least I hope it is haha.

 

[Nickie]

I understand your confusion and I'm happy to provide some insight to help you solve this problem. In order to determine the resultant moment at points A and B, we need to consider the forces acting on the truss and their distances from these points.

First, let's review the definitions of statics and moments. Statics is the branch of mechanics that deals with the study of forces and their effects on objects at rest or in a state of constant motion. Moments, also known as torque, are the twisting forces that cause an object to rotate. In this case, we are interested in calculating the resultant moment at points A and B, which is the combined effect of all the forces acting on the truss.

Now, let's focus on the forces that are perpendicular to the sloped surfaces. These forces can be resolved into their x and y components, just like any other force. The x component will act along the horizontal direction, while the y component will act along the vertical direction. This is important to note because the moment at a point is calculated by multiplying the force by its distance from that point and the perpendicular distance from the point to the line of action of the force. Therefore, we need to consider both the x and y components of these forces when calculating the resultant moment at points A and B.

For point B, the 10kN force will have both x and y components. The x component will be equal to 10kN, while the y component will be equal to 10kN multiplied by the sine of the angle of the slope (∅). This is because the force is acting at an angle to the horizontal plane, and we need to consider its vertical component when calculating the moment at point B.

In order to calculate the moment at point B, we will need to use the formula M = F x d, where F is the force and d is the perpendicular distance from the point to the line of action of the force. In this case, the perpendicular distance will be equal to the length of the truss (6m) multiplied by the cosine of the angle of the slope (∅). This will give us the perpendicular distance from point B to the line of action of the 10kN force. We can then multiply this by the x component of the force (10kN) to get the moment at point B.

I hope this explanation helps you understand how to calculate the resultant moment at points A and