Spring force due to Axial and Torque load?

[Mechaman]

Homework Statement

The first theory shows a spring under an axial load where the Torque is given as WRcos(a)

The second theory shows a spring under axial Torque. T is given as Wsin(a)

Homework Equations

Given in links

The Attempt at a Solution

A torque T would be at full strength along the X axis, where cos(0) = 1. Where a bending moment would be at full strength along Y where sin(90) = 1.

It seems to be other way around though, what am I missing?

 

[haruspex]

It seems to be other way around though, what am I missing?

In Fig 12.5, alpha is the angle between T and the Y axis, not between T and the X axis.

 

[Mechaman]

In Fig 12.5, alpha is the angle between T and the Y axis, not between T and the X axis.

Ok I see now how the axis has has rotated and has the same angle relative to the Y axis. So that means X axis is 0 degrees and Y is 90 degrees.

Why is the bending moment = Tcos(alpha) and axial Torque = TSin(alpha). Wouldn't measuring Torque be TCos(alpha) as Cos(0) = 1?

 

[haruspex]

Why is the bending moment = Tcos(alpha) and axial Torque = TSin(alpha). Wouldn't measuring Torque be TCos(alpha) as Cos(0) = 1?

The torque is around the X axis, so the vector is along the X axis, i.e. where alpha is zero. So yes, it is cos because cos(0)=1.

 

[Mechaman]

The torque is around the X axis, so the vector is along the X axis, i.e. where alpha is zero. So yes, it is cos because cos(0)=1.

Thanks for response sorry for late reply. I see now.