- #1
Svelte1
- 9
- 2
- Homework Statement
- dV/dx=-W
- Relevant Equations
- dV/dx=-W
How is the slope of the shear force equal to the negative of the load?
In summary, the shear force convention in the equation says that the slope should be positive, but in the shear force diagram, it is negative for any point between A and C. This is because positive is upwards in the diagram, while the point load is downwards. There may be some confusion with the sign convention for shear force, as it is used to oppose external forces on the beam to keep it static. However, in the paper shared by @haruspex, the shear convention is positive downwards, meaning the beam is deflecting downwards until a certain point, and then mirrors that deflection after. It is assumed that q represents a load in the equation dV/dx=-q, which is why the load convention is positive downwards. This
- #2
erobz
Homework Helper
Gold Member
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Personally, I don't think I've ever understood the shear convention myself. I thought it acts to oppose the external forces on the beam so that the beam remains static, but I'm not sure now. I look forward to hearing other's thoughts on the matter.
- #3
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At https://wp.optics.arizona.edu/optomech/wp-content/uploads/sites/53/2016/10/OPTI_222_W8.pdf, they seem to take q as a magnitude, and the equation dV/dx=-q is assuming it represents a load. Hence, effectively, the load convention is positive down.
- #4
erobz
Homework Helper
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So based on the convention given in the paper that @haruspex shared, the shear being positive from ##\rm{A}## until around ##x_1 = 5.7 \rm{m} ## where ##V=0## means the beam is deflecting like:
and after ##x_1## the beam in deforming like the mirror image of that:
and after ##x_1## the beam in deforming like the mirror image of that:
- #5
Svelte1
- 9
- 2
Ok, thanks guys. Assuming it's a load makes sens I suppose. Also I have a lot of questions around this level in the coming weeks, is this the correct forum for that? Thanks.
- #6
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Should be fine, but there is alsoSvelte1 said:
https://www.physicsforums.com/forums/engineering-and-comp-sci-homework-help/
1. What is shear force?
Shear force is a type of internal force that acts parallel to the cross-sectional area of an object, causing it to slide or deform in a particular direction.
2. How is shear force related to load?
Shear force is directly related to the external load applied to an object. As the load increases, the shear force acting on the object also increases.
3. Why is the slope of the shear force graph equal to the negative of the load?
This relationship is a result of the equilibrium of forces acting on an object. The slope of the shear force graph represents the rate of change of the shear force, which is equal to the external load acting on the object. Since the shear force acts in the opposite direction of the load, its slope is equal to the negative of the load.
4. How can this relationship be explained mathematically?
Mathematically, the relationship between shear force and load can be represented by the equation: F = -dV/dx, where F is the shear force, V is the load, and x is the position along the object. This equation shows that the slope of the shear force graph is equal to the negative of the load.
5. Is this relationship applicable to all types of objects?
Yes, this relationship holds true for all types of objects, as long as they are in a state of equilibrium. This means that the external load acting on the object must be balanced by the internal forces, including shear force, to maintain a stable and unchanged state.
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