Application of Influence Lines - Absolute Maximum Bending Moment (Series of Concentrated Loads)

In this question, we explore how to use influence lines to solve for the absolute maximum bending moment of a beam. In this question, we have a series of concentrated loads and must determine where the absolute bending moment is developed and the location of the loads when this occurs.
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[@AFMathandEngineering]

Click here if you missed our video on the easiest method of drawing influence lines! kzbin.info/www/bejne/Z3LcipqiiMpmn68

[@ibraheemsalkini3123]

You are very kind 😍🌹

[@cadebriar9921]

i know it is kinda randomly asking but does anybody know of a good place to stream newly released movies online?

[@desmondsimon6261]

@Cade Briar I watch on FlixZone. You can find it by googling =)

[@ronanzaid2154]

@Desmond Simon Yup, I've been using flixzone for since april myself :D

[@cadebriar9921]

@Desmond Simon thank you, I went there and it seems to work :) Appreciate it!

[@walidalaywan6385]

I do not see the reasoning behind x is equal to xbar/2. X = 14-xbar = 14ft. - 9.33ft. = 4.67ft. Though answers are too close.

[@rickyjohnsibog9304]

Same thought. Now I got confused. Hahaha

[@goodmanlukhele6873]

he got the right answer but he should have went with the simple logic of x= 14-9.38

[@mehdighasemi4528]

Thanks for your excellent information

[@vidyapatil2823]

sir really it is very helpful..thank you so much.

[@learnercivil8435]

I have a question. When you were trying to find the reaction at A... You took help of the resultant force to carry in the moment equation rather than using all the forces individually. Isn't that wrong ?? Shouldn't the equation of moment at B should have 16*something + 16* something + 4* something - Ra* 50 =0

[@AFMathandEngineering]

Thanks a lot for the comment :) I encourage you to try the method in which you use the resultant, as well as using the individual point loads when taking the moment about B and you'll see that you get an identical answer for Ay. Why? Because we located the resultant and determined its magnitude by the condition that the moment of the resultant about a point equals the sum of the moments of the individual loads about the same point.

[@learnercivil8435]

AF Math & Engineering yes. Ypu are right bro ! Thanks ..for such great videos and tricks. Please upload videos related to RCC designing and column buckling, asap. 🎉🎉🎉

[@AFMathandEngineering]

no problem, thanks for the compliment and the comments! we will add it to our list of videos to make, thanks again!

[@AFMathandEngineering]

Learner CIVIL also I forgot to mention, we do have some videos related to rcc design and analysis, check out our concrete playlists!

[@emilyreid9806]

I can understand that the 16k force and Pr should be equidistant from the center of the beam for maximum bending moment, but what's the justification for that? The video doesn't explain that point and I'm curious to know the proof behind it.

[@tjkulkute]

Great video. That's help me a lot. But could you guide me how to calculate the ordinate of each point load, then we can take each point load multiple with ordinate to get maximum bending moment. Thank you

[@AFMathandEngineering]

Hey, this video was on how to calculate the location of where to place the truck on a simply supported beam. It's related to the influence line of the support layout you have. The point loads themselves are spaced according to the given truck load from the code that you're supposed to design for.

[@tjkulkute]

Thank you for quick reply. Could you please make a video that show how to calculate the ordinate of series concentrated load of Influence Line Diagram

[@AFMathandEngineering]

Yes we will make a video on this topic,.thanks for watching!

[@ibraheemsalkini3123]

I am very thankful

[@brraian]

Hey thanks for the vid. I have a question tho. What is the logic behind placing the load such that the distance from it to the CL is equal to the distance from the CL to the Pr as shown in the vid? I understand the use of influence line but I can't seem to connect it with this calculation. Thank you in advance.

[@nurullfarah1437]

i have a question. why is the bending moment happen at the second load of the series??

[@AFMathandEngineering]

Very good question! So in this video, we place the load between the resultant and the nearest force on the maximum value of the influence line, and the maximum bending moment occurs under the nearest load. If you consider what the bending moment diagram would look like for a series of point loads, it'll be a series of linearly increasing or decreasing lines between the points, where the max will occur under one of the points. As such, this maximum is the load nearest the resultant. Try drawing the shear force and bending moment diagram for this configuration and I think it will be more clear to you. Also, if you have a structural analysis textbook, they usually have a good explanation and derivation of this concept. Thanks for commenting, hope that helped.

[@vincepiolodavid4920]

How about the max shear???? Can we use the right reaction to find the max shear???

[@AFMathandEngineering]

The max shear will occur at the support of a simply supported beam. Take the moment about one of the support, find the reactions and the larger is your max shear :D

[@vincepiolodavid4920]

Demm men thank you for this i got my final exam right!!!!!!! Bless u bro keep making videos

[@AFMathandEngineering]

Excellent man, glad we could help you! Let us know if you want any specific video topics and well add them to our list. What year are you in btw in school? Cheers!

[@vincepiolodavid4920]

Im in 4th year next semester, studying civil engineering

[@AFMathandEngineering]

Vince Piolo David excellent man good luck, let us know how it goes :)

[@jjmoncada]

Hello there, We were asked to consider the following: we need to place as many trucks possible on the beam. E.g. since this one is about 26 long, how many axis can you put on the beam? How would you find the maximum moment of the beam? Any help? Thank you!

[@AFMathandEngineering]

Hey there, it's an interesting question, it depends if the beam is simply supported. I know in the Canadian bridge design code, they make you design for a uniform load (assuming the bridge is stopped in traffic, so the bridge is full), and a truck (the type of truck, axle layout and load is specified in the code) placed as to create the maximum moment plus a dynamic load factor due to the movement of the one truck. You'd need to be given the amount of axles, space of how many trucks could fit on the bridge, etc...seems like a strange question heh.

[@vincepiolodavid4920]

Teach me for our next sem, ULTIMATE STRENGTH DESIGN PLS :D

[@AFMathandEngineering]

That's a good idea, do you mean ULS (ultimate limit state)? Maybe well do a video on the different limit states.

[@emmarizza2053]

thank you so much!

[@alkawther9376]

Is the concreted load a wheel load or truck load ?

[@AFMathandEngineering]

axle load of a truck

[@alkawther9376]

@@AFMathandEngineering I'm sorry I mean axel load or wheel load. Thanx to much

[@skatershawn410]

based on your moment direction you used the wrong sign when summing the moment at B.

[@AFMathandEngineering]

Yup, you're right. The answer ends up being the same regardless, but yeah that's a good find, thanks for your feedback. We will make a note of this.

[@skatershawn410]

Also, how again did you determine the max load was under the 16k? I have a problem with 4 point loads and I'm unsure.

[@AFMathandEngineering]

With 4 loads it can get trickier as you may have to check both. If you've taken any bridge design courses, or will take them, this is a very common topic in these classes. Typically, the largest load, assuming the adjacent loads are equal or smaller than it is the one where the maximum moment will typically occur. However it may not always be this clear; if you have a structural analysis textbook there's a much longer explanation in that section that you'll probably want to go over. If you scroll below, someone asked as well why the max moment occurs under the highest load, and I gave a relatively detailed explanation on that if you'd like to read it. Hope that helps.

[@zeyadsbaih6073]

What if the the truck is taller than the beam , how we will calculate the resuiltant force ?

[@AFMathandEngineering]

Sorry, what do you mean by "if the truck is taller than the beam?"

[@zeyadsbaih6073]

AF Math & Engineering i mean the truck lengh if it bigger than the beam span Lets suppose that the beam spam is 4 m And truck is 6m , then some forces will be outside of the beam , how we will compute the resuiltant? Or how to deal with this case

[@AFMathandEngineering]

Oh, I see. In that case if all axles dont fit on the bridge, you'll need to use two axles instead and place them in the same place like we did in this video.

[@AFMathandEngineering]

zeyad sbaih if you're in civil engineering and you take a course on bridge design you'll definitely go over this subject in detail.

[@zeyadsbaih6073]

If i have 3 axle and two of them only fit , the resuiltant will be calculated from the two axle or all of them ?

[@gabrielpineda9144]

you said this is an application for influence line, yet you didn't even use the influence line of the beam ?

[@AFMathandEngineering]

This is an application of influence lines, where the truck is placed is based on the influence line of the beam, we just didn't draw the influence line itself.

[@KamalAlogla]

I am sorry to say that your calculation is wrong, because the absolute maximum moment in a simply supported beam occurs under one of the concentrated forces, such that this force is positioned on the beam so that it and the resultant force of the system are equidistant from the beam’s center-line ....

[@AFMathandEngineering]

Before making accusations, you should probably listen to and watch the video more carefully. At 7:47, we clearly state that the maximum bending moment happens under the second axle. This is obvious, as the bending moment will take a linear shape, with a peak occurring at one of the point loads. However, as you can tell from the start of the problem, the question asks to find the maximum bending moment of the truck and the truck's location is not given. You most likely confused yourself by thinking that the steps we used to locate trucks position that would yield the maximum bending moment was where we were locating the moment. We never mind constructive criticism, but try to show some humility rather than not really watching or listening to the video and declaring yourself correct and everyone else wrong.

[@wtf4540]

where is the influence line hahaha