Combined Loading 3-D Example (Part 1) - Mechanics of Materials

In this video we calculate the state of stress at a point in a rod that experiences a state of combined loading (i.e. internal normal, shear, and bending moments are present about multiple axes).

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[@structurefree]

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structurefree :)

[@structurefree]

positive y moments are in the direction your fingers curl when you point your thumb in the +y direction. so the 600*12 rotates in the opposite direction as your fingers, therefore it is negative.

[@Virusruneblazer]

Thank you so much I have a statics and mechanics final tomorrow morning and you really cleared the air on combined loading! Very clear video

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You are the best, so funny and just such a great teacher. 3D combined loading was lost on me until I discovered this! All the other videos are amazing too!

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[@lawrencemiller1811]

"It's normal. Just like me!" Hahaha. That part got me laughing. thanks for the extreme help!

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[@mohamadhasrulrezamohdhisha8798]

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[@structurefree]

@Panth Naik as long as you also calculate the internal moments and torque at the cut, you will get the same result. It is not really superposition that is being applied, rather the six equilibrium equations.

[@cxh970712]

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[@El_inge_987]

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[@ΔημητρηςΒροχαρης]

As far as i am concerned , there are no shear stresses at the periphery , the shear stress profile is parabolic.

[@ΔημητρηςΒροχαρης]

@@lwthorn1977 yeah probably otherwise the solution has gone wrong .. anyways , most times shear stress can be omitted due to their small contribution to the result and the percentage of this fault comes to a 2 or 3 percent ... actually most times i use tresca or vonmises criterion and it doesnt bother me somuch

[@TJWaterFlows]

At 6:40, why is the 600*12 being subtracted, while at 5:45, a positive moment is induced when 600*8 is added to Mx? Thanks in advance - it's a very helpful video.

[@DRLED-pd7pu]

For anybody reading this. He messed up sign convention here. Use Right Hand Rule

[@jkgao97]

I mean, as long as he sticks with that convention, it's alright.

[@structurefree]

i'm glad it helps.

[@theengineeringlife9451]

Thank you for the great video sir, how do we know when to use the correct shear vs stress equations. For example, for Ny, how do we know that normal stress is N/A and not Mx/y. Same goes for the shear equations. Also, when do we apply both equation for both stress n strain. Really struggling with this concept

[@gkrozr9]

12:25 Can you please explain why you took this area, wasn't Q above or below

[@omarzain6050]

Gkrozr Vx.Qz/Iz so he uses the left or right area but if it was Vz.Qx/Ix he will use the upper or Lower area

[@gkrozr9]

Omar Zain Thank you.Appreciated :)

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writing my mechanics of materials exam tomorrow,feeling confident thanks to you bro!

[@notSavant]

Can you explain the reason why you chose those interanl loads in the begining?

[@diao1111]

Hi there, can you evaluate more on the Moment equilibrium equations as I cant quite get my head around that. Why is Moment about x only caused by the 600 lb? and for moments about y and z respectively

[@silentprayers728]

I'm more interested in drawing an infinitesimal element cube with arrows for axial, bending, transverse shear, and torsional shear. A problem that is more conceptual, drawing at different cross sections at different points (ex. top of cross section, side of cross section, etc.)

[@structurefree]

Good idea!

[@NoorFarhat]

Is there no continuation of the video? Awesome part 1!

[@DarthYoungling]

Your videos, I physically smile... Comment fail.

[@MrZiiiro]

Great teacher ! very helpful videos..

[@structurefree]

Thank you! You are too kind.

[@Mrjrphoen]

Your lectures are excellent chief. I thought 1st moment of area, Q, for V_x should be all area below pt. B or above pt. B as mentioned on the earlier 2D example, so shouldn't be the whole circle instead of half?

[@structurefree]

It is relative to the direction of the internal shear force you are looking at. Thank you for the kind words! Good luck with school!

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You are a life saver, Thank you every much!

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Thank you very much

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Which one off your videos do you recommend i apply for the lift arm of a Skid steer loader connected to the chasis at one end and connected by pivot to a bucket with load at the other end

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Thank you for the kind words. I'm actually more flattered that you think I'm funny. Congratulations on all your success!

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[@amatoallahouchen5894]

thank you for the amazing video, should not the shear stress on point B( on the surface) be zeo because shear is caused by forces between layers! thank you!

[@elaysiasimms8882]

how did you compute the moment forces about point z? im not understanding how you know to multiple for that particular axis.

[@911Teresa911]

How do you know when it was shear stress and when it was normal stress? I know normal has to on with it being perpendicular to the force and shear has to be parallel. So why is Mx in normal stress and not shear? and same with the rest. THank you

[@structurefree]

911Teresa911 bending moments have a tension and compression force couple which are normal to the surface and cause a normal stress, they also cause elongation and contraction which are associated with normal stress. Twisting moment or torque cause angle changes which are associated to shear stress.

[@panth92]

Will the sign of the compressive or tensile force not be different at the cross section giving you a different normal force number for that cross section?

[@goldilauks]

I wish you were my teacher.

[@DailYxDosE]

12:48 what is Q the left shaded half of the circle and not the half circle above Vx?

[@adlee0705]

Normal, just like me! haha, make me laugh so loud. Btw, great explanation!

[@structurefree]

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[@magdkhalid8366]

structurefree

[@aurey997]

12:59 why is that half of the circle??

[@patrykmuter28]

fantastic material my homies

[@aga080]

thank you

[@dwkrnpl]

why is it shear stress and not normal stress? can you explain how to distinguish(pick) what type of stress it is

[@floormatt3]

+deepak np remember that shear is across a surface, normal is into a surface. So if you look at the force of y in this example, it goes into the surface therefor it is normal stress. If you look at force of x, it goes sideways, therefor it will cause shearing.

[@ItsTopCat]

floormatt3 omg ty so much!

[@massimobaldini5912]

You just saved a very frustrated student!

[@FawazBnMohammed]

12:25 explain why you took this area, you said before Q is above or below i hate it when this happens

[@ahmedalawsy9485]

Last minute life saving

[@de-SportsHub]

you say compression, normal or shear but you failed to explain why those points/faces are experiencing such forces.

[@theskijunkie]

If you view his other prequel videos, all of that is explained.

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Do you have a site or channel with mechanics of aerostructures video lectures. very similar to this

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what topics are you looking for? fiber reinforced polymer composite mechanics?

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structurefree here are a list of the topics am looking for www.colorado.edu/engineering/CAS/courses.d/Structures.d/

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I cover some of the strain/stress concepts, torsion, and beam deflections in my mechanics of materials playlist. Unfortunately, I have yet to add the other topics...I'll add them to my to do list.

[@joshuagerman8579]

Thanks. I ll appreciate that so much

[@panth92]

Quick question , at the beginning of the problems why did you not superposition the applied forces to the cross section at b. Hence giving vx=-500,vz=600, and ny=800, then going from there. Thats what my textbook does, they just take the applied force and put it onto the cross section of where we are looking at. Does your method and my method give the same result in the end?

[@yangli3645]

it is really helpful.BTW, what software are u using?

[@nilufargh]

Thank you so much! but why did you consider only half of the circle to find Q?

[@aliabbas2138]

i also cant understand that part can you make me understand it

[@osamawali1098]

@@aliabbas2138 q is calculated for only one side of the point for which you are calculating the shear which is the shear formula requirment

[@RH2022A]

Love you man

[@IMrajnishsingh]

There should be a torque at the cross-section about y axis due to the 600 lb force or am I wrong?

[@structurefree]

+Rajnish Singh Yes, there is. It is labeled as My in this problem.

[@IMrajnishsingh]

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[@brianwin5183]

Thank you.

[@lisro21]

Man you are saving my ass.

[@nicolef4552]

For part 3, when you find the normal force due to Mx, how did you know it was a normal force and that it compresses point b. I just cant quite visualize this piece. Thank you

[@bzq3386]

Visualize it as a beam bending. The moment about the x-axis is due to the 600lb force. Its causing compression at the top (where point b is) and tension at the bottom. In simple words visualize this as a smiley face. Top in compression and bottom in tension. Hope this helps.

[@nicolef4552]

@@bzq3386 Thank you! This helped me realize to look at it in its entirety, not just the cross-section. Because if you think about the rotation the 600 lb force will cause, it will go through the plane of the cross-section. Thank you again

[@bzq3386]

@@nicolef4552 Welcome!

[@nickknauer15]

Thanks, very helpful

[@lildefa]

If you've got normal force in Y direction, wouldn't it be torsion instead of moment about that axis?

[@gokujoseph1180]

how do you calculate the moment equations. can you explain how to do it. i can do it in two -d but i cant wrap my head around how you do it in 3d

[@eduardourbano3967]

What is the book used? Idk what is the whole question.

[@zhengyangsong]

Many thanks in advance!!!!!!

[@othescientist]

Shouldn't all of your signs be flipped if you are considering the stresses at B resulting from the applied forces? i.e. You are finding the internal forces and moments that balance out these forces, but you're considering the left side of the cut when your proper sign convention would result from considering the right side of the cut. Gnomesayin?

[@floormatt3]

+Fricks and Fracks No, when you write out your equilibrium equations you will find this. In this example, when finding Vx, you would write out the equilibrium equation as follow: Fy = 0 = Vx - 500 => Vx = 500. This Vx is headed the opposite direction, and therefor balancing like you say. There is no need to switch the signs once you've found your forces.

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very helpful

[@jadfahed7991]

Love u bro u saved me

[@structurefree]

yes.

[@einstienalbert5146]

Hello, Can anyone please help me in understanding ,How to take moment about any axis?

[@notSavant]

Is the formula you use for the shear stress not for other shapes?

[@mysticflickr7348]

Hi, Actually what to do when the cross section is of Hexagon and not circular. I have an assignment of allen wrench in which we need to follow combined stress method to check the convergence between hypermesh and Mechanics of material results. I can send the pic of problem if i get an email id if you provide. or anyone who can help with the topic

[@nickknauer15]

When you are solving for My, why are you subtracting 600(12)?

[@TeamLakers24]

OMG...goddamn memories lane. Just graduated...n idk how i survived through all this.

[@panth92]

Wait I think I understand now. My signs are basically opposite then yours , but they should give me the same answer. While my compressive normal force is positive, yours is negative, and while my moments are positive or negative , yours are the opposite sign. But they should give me the same answer, is that correct?

[@NinjaNicX]

Thank you so much!

[@benjaminshiflett8066]

wouldnt Vx be 0 at B due to its distribution? max at neutral axis and 0 at edges?

[@jasonlatimer55]

This guy is hilarious.

[@shawnnjh]

Is there a confusion between moment and torsion? The way i see it, for the x-axis: 600*8 is the torsion while 600&12 is the moment, please clarify.

[@floormatt3]

+Shawn Ng No, the torsion happens along the normal axis. Basically, if you draw out your cuts like he did the torsion should make a clockwise/counterclockwise arrow. In this example, that only happens along the y-axis and not the z- or x-axis.

[@3dprintkkstudio]

why Q only take half of the area of circle?

[@osamawali1098]

its torque about y axis not moment right?

[@kamals4905]

is that possible to add(combine) two mechanical force(torque) Ex:- if i have two 1.5v batterys >> - if i connect in series the voltage increase OR - if i connect in parallel current rating is increase same as in mechanically either rpm increase or torque increase i dont know is that good question or silly one........hahahah but please replay me if you have any suggestion

[@kimDONDE]

how to identify moment -600(12) or +600(12)?

[@theadel8591]

you forgot to include the shear stress at point B due to the torque (moment about y-axis in this example).

[@leakedazaz]

keeping things straight is what I do best!

[@jafaraldahan4176]

YOU ARE PERFECT

[@yamikawaii321]

Why Vx induce shear stress at B not at A?

[@thebluestbelly]

thanks man you saved my ass

[@juliangarcia3416]

Why 600lb induces a moment in x directrion?

[@DeenQuery]

great stuff; you're awesome :-D

[@gregmiller8135]

Ive spent a lot of time on trying to understand internal loadings, and I want to know why you ignore equilibrium sometimes. Why do you have a negative normal force? I feel like that isn't possible. I also feel like a negative moment reaction is impossible. Can someone clarify?

[@leeshanpillay1253]

It is not impossible. It is negative because it has to counteract the other forces in the positive direction to reach equilibrium. I dont understand how to take moments in 3D any suggestions?

[@ephraimmoye4772]

I wish you were my lecture.

[@xhuliomyftari8039]

Isn't the 600 lb producing a Torque?

[@charlesbobby7092]

Why do we only care about the x axis and y axis, as opposed to all 3 (including the z)?

[@osiksama]

tqvm sir..

[@matheustf2867]

Part2?

[@hzeeq98]

how to know whether to put minus or plus sign for moment eq????? pls someone help meeeeeeeeeeee

[@jameshiller678]

when finding the moment around the z axis, the 500(8) part should be negative

[@stephanehentzen5662]

No, it's positive. Apply the right hand rule along the z-axis.

[@sharmaenrameshwaran6498]

But it is supposed to be negative once I used the right hand rule along the z-axis

[@sharmaenrameshwaran6498]

Oops didnt notice the direction of force carefully. Sorry