Is Shear Force Always Maximum When Moment is Zero?

In summary, the statement that when the shear force is 0, the moment is maximum is not always true. In some cases, such as in a cantilever beam, both the shear force and moment can be 0 at the free end. The author may have been referring to the possibility of the shear force being 0 at a location where the bending moment has a relative maximum or minimum.
  • #1
chetzread
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Homework Statement


in the book , i was told that when the shear force is 0 , moment is maximum . However , in this question , i found that when the shear foce is 0 , the moment is also 0 . I'm wondering is the ststemnet true ?
swF2bVW.jpg


Homework Equations

The Attempt at a Solution

 
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  • #2
chetzread said:

Homework Statement


in the book , i was told that when the shear force is 0 , moment is maximum . However , in this question , i found that when the shear foce is 0 , the moment is also 0 . I'm wondering is the ststemnet true ?
swF2bVW.jpg


Homework Equations

The Attempt at a Solution

Obviously, if the beam is a cantilever, the shear force and the bending moment can both be zero at the free end. You won't find the maximum moment there in any event.

I think what the author was trying to say was that since the derivative of the bending moment, dM/dx = V, the locations where the shear is zero are also possible locations where the bending moment has a relative maximum or minimum.
 
  • #3
SteamKing said:
Obviously, if the beam is a cantilever, the shear force and the bending moment can both be zero at the free end. You won't find the maximum moment there in any event.

I think what the author was trying to say was that since the derivative of the bending moment, dM/dx = V, the locations where the shear is zero are also possible locations where the bending moment has a relative maximum or minimum.
so , for the above case , shear force = 0 , moment = 0(minimum) ?
 
  • #4
chetzread said:
so , for the above case , shear force = 0 , moment = 0(minimum) ?
Obviously.
 
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1. What is shear force?

Shear force is the force that acts parallel to a surface, causing it to slide or shear. It is the result of applied loads on a structure or object.

2. How is shear force calculated?

Shear force is calculated by summing all the external forces acting on a section of a structure or object and taking into account the direction of the forces. It is usually represented by the symbol 'V' and measured in units of force, such as Newtons (N) or pounds (lb).

3. What is moment in engineering?

Moment, also known as torque, is the measure of a force's tendency to cause an object to rotate around an axis. It is calculated by multiplying the force by the distance from the axis of rotation. Moment is usually represented by the symbol 'M' and measured in units of force multiplied by distance, such as Newton-meters (Nm) or pound-feet (lb-ft).

4. How are shear force and moment related?

Shear force and moment are related in that they are both measures of the effect of external forces on a structure or object. Shear force causes a structure to slide or shear, while moment causes a structure to rotate. They are both important considerations in structural design and analysis.

5. What is the difference between shear force and bending moment?

The main difference between shear force and bending moment is the direction in which they act. Shear force acts parallel to a surface, while bending moment acts perpendicular to a surface. Shear force causes a structure to slide or shear, while bending moment causes a structure to bend or deform. They are both important factors in determining the stability and strength of a structure or object.

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