# Moment of a force in 3D

The question is not to help me get my task completed. There is the 3D statics problem that I have been attempting to solve for a long time. I have no help, hence I would like to pose you a few questions to ensure I am on the right road to end the task.

Some translations: silinder means cylinder (a kinematic pair - joint); sein is wall, and ramp stands for ramp in English. A white sphere is a vehicle, whose mass is defined as a force $$F_v$$ - the cylinder has it, but we neglect it, because $$G_s \ll G_r$$ and $$G_s \ll G_v$$, so we set it to be nearly equal to zero.

The task is to determine reactions at A and C.

As my lecturer states, I have to write the equilibrium equations, starting with the moments of forces. If I write the equation for moments at A about the axis $$x$$, then I get $$R_C$$. Also, he informed that the reaction at B is none or, equivalently, there is no reaction at B. Okay, we are going to determine the resultant vector of the system, given by $$\vec{R}=\sum_{n=1}^{m}\vec{F_n}=\vec{R_A}+\vec{R_C}+\vec{F_v}+\vec{F_h}=0$$ From this equation, we get the connection between $$R_A$$ and $$R_C$$. Moreover, we find $$Y_A = F_h \sin \alpha$$, because $$Y_C = 0$$, seeing that it forms the angle $$\pi/2$$ with the axis $$y$$. - This my first mistake: $$R_C$$ forms the angle $$\beta$$ with the plane $$xy$$, hence $$Y_C \ne 0$$

Proposal 1. We can reduce the system to the point $$A$$ by determining the main vector and moment. Setting them to zero, we acquire equations.
Proposal 2. I tried to bring the problem to the one which I know how to solve; in other words, I know how to solve 2D beams, why not consider the problem as a complex one. That is, I wish to consider the planes $$xy$$, $$xz$$ and $$yz$$ separately. On which plain, I can compute moments through points. For that, I project all forces onto the planes and consider the equilibrium of each part.
This might be of help to construct diagrams of bending moments in 3D beams - this is my conjecture.

For those, who are interested in the task: On the picture, the lifting, inclined ramp with the braking vehicle is depicted. We assume that action is with the emergency load situation, where there is one lifting cylinder and one pivot (hinge) is broken. The vehicle weighs about 2.5 tons and we assume that while it is braking, the force $$F_v$$ become maximum $$F_h = 0.3 \cdot F_v$$. Ramp itself weighs10 tons and cylinder weight can be neglected. Determine reactions at the points $$A$$ and $$B$$. The width of the ramp is $$b$$ and the length of it is $$l$$. Hing $$A$$ and cylinder attachment $$B$$ are at the distance $$b/2$$ from the mid axis (centroid axis). The angle between ramp and cylinder is $$\beta$$. We also assume that the vehicle is at the distance $$b/4$$ from the centroid axis and at the distance $$3l/4$$ from the wall. At both Cylinder's ends on spherical pivot joints.

• I think you have significant errors in your translation. Better double-check it. if the only support of the ramp at the wall is A, then the ramp will rotate towards us. C does Have a Y reaction. What is the white Fh? What is the angle alpha? – kamran Oct 19 '20 at 5:55
• @kamran I thought the same regarding A, however it seems that there is pivot there which allows rotation only around the horizontal axis (maybe a long pin joint). However, that still leaves the problem of joints B and/or C. I think the only way this can be solved is if C is a universal Ball Joint. Otherwise its indeterminate – NMech Oct 19 '20 at 6:20
• If the hinge is broken (probably at the point B), then begs the question if there is incorrect reaction $R_B$ that still connects the cylinder with the wall due to nonstandard or deformed pivot at B? – sergei ivanov Oct 19 '20 at 7:49
• Thus, the question is about the problem I have encountered (description on the post). I have realized what is torque about an axis of rotation via a point. The point can lie only the axis and nowhere except for the place, otherwise the torque has no sense. Now I can write equations for the moments. I would like to apologize for unclear question. I edited it until it became more clear – sergei ivanov Oct 19 '20 at 8:35
• I do not know about moments or torques at B, but there is the reaction $R_B$. All questions that I posted on the forum I shall attempt to answer by means of the task. I have answers for the task (called the third homework, which is not obligated and optional), therefore I might tell them to you, should you have solved it. – sergei ivanov Oct 20 '20 at 16:59