# Torsion and deflection of a rectangular beam

• Engineering
• dbag123
In summary, the angled bit of the beam moves things to account for deflection and torsion. The calculations for the torsion are incorrect.
dbag123
Homework Statement
calculate the total displacement of the angled part. deflection and torsion
Relevant Equations
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Hello
I would like some feedback about a problem. The idea is to calculate how much the angled bit of this beam moves things to account for are deflection and torsion. Did i miss anything?

Underlined with red are the displacements in millimeters.

In the picture the dotted line is the axis that the beam twists about.

#### Attachments

• 1571427319573.png
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It= torsion constant
Mt= Moment caused by torsion
Theta = torsion of the profile in rad for every mm
Phi = Total amount of torsion for the section
y= displacement caused by torsion

I don’t know where you are getting values for e and x. Please explain.

e = the length of the handle (90mm)

x = the leftover distance. (triangle side b-handle=95mm)
The angle of the bend is 45deg, so those 2 sides of the imaginary triangle are both 185mm, so 185mm-90mm(handle) = 95mm

yes, same object different problem

Let the x-axis be horizontal, y-axis vertical, and z axis out of plane in direction of handle. The load F is applied vertically down along y axis. I thought we agreed for torsion at say the fixed end the torsion moment is Fz = 150 (110), right?

that is true, for torsion at point of rotation (fixed point). However the perpendicular distance to the acting force in this case(looking at the angled part only) according to my calculation should be 95mm, and the torsion moment 150(95)

The total deflection of this angled bit should be very small, and i know that deflection due to anything has a lot to do with the length of the object being bent

Last edited:
Oh, the angled beam, OK, but you are not calculating the torsion on the angled beam correctly. If you extend the longitudinal axis of the angled beam (as you have done , making it the hypotenuse of the 185/185 legs), then the torsion on the angled beam is the Force of 150N times the perpendicular distance from that force to the extended angle beam axis, which I calculate as (150)(95)/SQRT 2.

PhanthomJay said:
Oh, the angled beam, OK, but you are not calculating the torsion on the angled beam correctly. If you extend the longitudinal axis of the angled beam (as you have done , making it the hypotenuse of the 185/185 legs), then the torsion on the angled beam is the Force of 150N times the perpendicular distance from that force to the extended angle beam axis, which I calculate as (150)(95)/SQRT 2.
do you mean like this?

the x distance?

Yes!

Allright. what about the displacement in mm? y=x*sin(angle), I am guessing the x distance also changes from 95 to 67,2mm

my brain is getting fried with this problem.

The deflection from bending moments in the angled beam is more than PL^3/3EI, because there is also a bending moment couple applied at the end where you are calculating the deflection.
Now there's twisting going on all over the place, much of it just rotating the beam section without vertical deflection, but I think that vert deflection in the angled beam from twisting moments is governed by the twist angle at the critical section at the cantilever end, which can be ignored since it is small. I'd have to think more about this while you do the same.

## What is torsion in a rectangular beam?

Torsion in a rectangular beam refers to the twisting force applied to the beam, causing it to rotate about its longitudinal axis. This can occur when an external force is applied to one end of the beam, causing it to twist in the opposite direction.

## What is deflection in a rectangular beam?

Deflection in a rectangular beam refers to the bending or displacement of the beam when subjected to an external load. This is caused by the internal stresses and strains that occur within the beam, and can affect the overall stability and strength of the structure.

## What factors affect the torsion and deflection of a rectangular beam?

The torsion and deflection of a rectangular beam are affected by several factors, including the material properties of the beam, the dimensions and shape of the beam, the type and magnitude of the external load, and the support conditions at the beam ends. These factors can all impact the strength and stability of the beam.

## How is the torsion and deflection of a rectangular beam calculated?

The torsion and deflection of a rectangular beam can be calculated using various equations and formulas, depending on the specific properties and loading conditions of the beam. These calculations typically involve determining the internal stresses and strains within the beam, and using these values to calculate the amount of torsion and deflection that will occur.

## How can the torsion and deflection of a rectangular beam be reduced?

The torsion and deflection of a rectangular beam can be reduced by using materials with higher strength and stiffness, increasing the dimensions and cross-sectional area of the beam, and providing additional support or reinforcement at critical points along the beam. In some cases, redistributing the load or changing the shape of the beam can also help to reduce torsion and deflection.

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