How Do You Calculate Shear Force and Bending Moments in Stub Axles?

[jonny2k]

i have been set a question to draw the shear force and bending moment diagrams for the loading condition shown on the diagram, and am not quite sure how to do this...

do i need to work out other forces along the diagram?

and help...much appriciated thanks!

 

[ctjen]

This is a basic cantilever beam with a point load.
The shear force will be the same between the point of application of the load and the reaction to the load. The bending moment (force x length) will vary linearly with the distance from the load to the reaction to the load. The axle's variable geometry (indicating a non-prismatic beam) effects the distribution of internal stresses. The load diagrams are determined only by the nature of the loads (point, distributed, etc.) and the position and nature of the supports (free, pinned, fixed).

Chris

i have been set a question to draw the shear force and bending moment diagrams for the loading condition shown on the diagram, and am not quite sure how to do this...

do i need to work out other forces along the diagram?

and help...much appriciated thanks!

 

[jonny2k]

with the axle fixed on the right hand side does this mean the only shear force is where the force is acting (in the centre of the 3rd block)?

 

[ctjen]

with the axle fixed on the right hand side does this mean the only shear force is where the force is acting (in the centre of the 3rd block)?

No. The shear force is acting on every arbitrary section between the point of application of the force and the reaction to the force at the right hand side. It's not just at the point of application of the load.

Chris

 

[jonny2k]

so the force acting on each section is different? this is what's confusing me i think! how do i work out the different forces say at 6 points along the axle...

 

[ctjen]

so the force acting on each section is different? this is what's confusing me i think! how do i work out the different forces say at 6 points along the axle...

The shear force acting on each of the six points is the same. It is the same at any point on the axle between the point of application of the force and the point of resistance (reaction) to the force. You're imagining that the six points where the geometry changes have a special significance in regard to the shear force when they don't. The shear stress in the axle referenced along it's length does vary according to the cross sectional area at each point of interest. The geometry does come into play when looking at stress (force /area). If you had to draw the shear stress diagram then your concerns would have merit...but you're not being asked to draw the shear stress diagram. You're being asked to draw the shear force diagram. The shear force is constant and equal to the applied load at every possible vertical cut you might make in the axle between the point where the load is applied and the point where the load is resisted at the right hand end.

Chris