cunning prism
So this is the picture of the task i am really confused how to find this equation cause i have no idea how this loads works.. i have cheked the books for it But the load and stuff is like the math part of the mechanichs part and we dont have that before next year so my math book doesnt mention it idk What i am supposed to do to find it really
solid carbonBOT
So this is the picture of the task i am really confused how to find this equatio...
+close
honest lynx
To write the equation for q(x), which represents the distributed load as a function of z, we should rather consider the different sections of the beam. For 0 ≤ z ≤ |1, the load is constant at q0, so the load function would be q (z) = q0. For |1 ≤ z ≤ |1 + |2, the load linearly decreases from q0 to 0 over the length |2. Equation of a line between the points is q (z) = q0 ( 1 - z - |1 (divided by) |2. Where z is the distance from the start of the section. For |1 + |2 ≤ z ≤ |1 + |2 + |3, there is exactly no distributed load, so q (z) = 0. This function describes the distributed load q(z) along the beam.
btw, the | is the dimension line if you were confused with that.
cunning prism
To write the equation for q(x), which represents the distributed load as a funct...
I am not only confused with that Line sorry… i am confused with everything can you please explain it with less < and > and all that cause i am really clueless as to what to do
Also sorry if i seem verry verry stupid and give the impression i cant read But english is not my native language, i am bad in math and dyslexic, please dont Get triggered by my stupidity you Are warned now
honest lynx
Also sorry if i seem verry verry stupid and give the impression i cant read But ...
Sure thing, no problem. Basically, the beam is divided into three directions based on the distance along its length (denoted as z). So, for the first section (0 to |1), the load is constant, and the value of load is q0. So the load function is q (z) = q0.
For the second section (from |1 to |1 + |2), the load gradually decreases from q0 to 0. The load decreased in a straight line, so the load function is linear. The equation, again, for the load is q(z) = q0 ( 1 - z - |1 divided by |2 ).
Lastly for the third section (from |1 + |2 to |1 + |2 + |3), there is absolutely no load at all, so q(z) = 0.
If this also gets confusing for you, let me know, as I tried my best to evaluate it.
And again, the | is the dimensional line.
cunning prism
I have a feeling inmisunderstood
honest lynx
So like it would be 3 equations i need?
Exactly, each equation of the beam, since the load changes in each region.
honest lynx
I have a feeling inmisunderstood
Your on the right track for the 1st and 3rd equation, but the 2nd equation needs a small fix. The equation should reflect that the linear decrease starts at z = |1 and ends at z = |1 + |2. Z is the main problem, for your working out, as it’s not perfectly adjusted for the start of the second section |1. Therefore, the correct equation must be
L2 = q0 ( 1 - z - |1 divided by |2. )
• |1 is the start of the second section
• |2 is the length of the section.
And also the 1 is separate to the division.
cunning prism
Your on the right track for the 1st and 3rd equation, but the 2nd equation needs...
Wait what does the 1 and 2 tell me here
honest lynx
Wait what does the 1 and 2 tell me here
Specifically in which section?
honest lynx
No no it’s not 1-z-, 1 is supposed to be separate from z - |1 / |2
I didnt point that out clearly.
honest lynx
Wait what does the 1 and 2 tell me here
1 in the equation balances the starting point of the second section.
2 decides the total length of the second section and scales the decrease in the load.
cunning prism
Hmmm i am sorry i am really not sure
cunning prism
No no it’s not 1-z-, 1 is supposed to be separate from z - |1 / |2
Still this i am sorry i am not able to picture How Its supposed to look like
Or the progress to Get There
I thibk someone mentioned it would be easier to Get it to like a point load instead of even load by taking the kN/m and multiply it by the length and then divide it by 2
And the task says 12kN/m and 3 meter
So is it correct with 12kn/m *3m / 2
honest lynx
So is it correct with 12kn/m *3m / 2
Oh yes exactly. The distributed load is 12kN/m, and the length is 3 meters
cunning prism
yes
honest lynx
Still this i am sorry i am not able to picture How Its supposed to look like
I just did it using Google.
So like this
cunning prism
I just did it using Google.
so the one is just a 1 it will always be 1 no matter what. then the z is the lenght(3m) and the other one is ? and the 2 is beacuse its a triangle and not a square ?
honest lynx
The 1 will not always be 1. It marks the start of the second section where the load also starts decreasing, it can vary based on where the load begins to decrease.
The z is the distance or position in the beam.
The 2 is there because the load is triangular and not a square or rectangular. Therefore it affects how the load decreases over the length of the section. The 2 just adjusts the fact that you are dealing with a triangular load distribution. Additionally, it isn’t a uniform load either, and if it was a uniform load, for example a rectangle, you wouldn’t be dividing by 2.
cunning prism
i am so sorry... i dont get the 1 and z and the second 1
honest lynx
I just did it using Google.
This is the equation, correct?
cunning prism
i think so
honest lynx
This describes a linearly decreasing load along the beam.
I’ll do this step-by-step.
cunning prism
thank you so so so much
honest lynx
The “1” in the equation represents the starting point, where the load begins to decrease.
cunning prism
how do i see that the 1 is supposed to be a 1
honest lynx
So, let’s say you have a beam, and the first section, constant load, ends at z = 1.
cunning prism
but there is no numbers on the z axis
honest lynx
So, let’s say you have a beam, and the first section, constant load, ends at z =...
This means the second section starts at z = 1, so then the load decreases from this point.
cunning prism
hmm is it beacuse of the L1 that i see its 1
so if it decreased at L2 it would be 2
cunning prism
Basicly like this
honest lynx
Yup, now this makes things much clearer.
cunning prism
ugly drawing but you get the point? if it decreases from the point of 3 its 3 and so on
yeah this make more sense sorry that i have to get it exlained so basic i am super gratefull that you are sooooo patient
honest lynx
ugly drawing but you get the point? if it decreases from the point of 3 its 3 an...
Eeexactly.
cunning prism
so in this task the distance is 3 meter for l1 and 3 meter for l2 and 0,6 meter for l3 does that mean its gonna be 3? instead of the z
or am i confused
cunning prism
ohhh and the second 1 is 1 beacuse thats the point its decreasing from again?
honest lynx
Yup, exactly
cunning prism
so lets say it was decreasin from point 2
its 2-(3-2)/(2)
oh no 0.6 isntead
but yeah??
honest lynx
Yup, if the load is decreasing from point 2, and you are now considering the length of the third section L3 = 0.6, the equation would account for the new equation.
You’re almost there
honest lynx
Is that 0.6 or 0,6?
cunning prism
ahhh it doesnt work lol
cunning prism
Is that 0.6 or 0,6?
sorry whats the diffrence
honest lynx
0**.6 is 0 point 6, 0,**6 is 0 comma 6
cunning prism
then the comma i guess
honest lynx
Alright anyways, is this what you want to show?
cold dustBOT
Henriette
honest lynx
Hm
honest lynx
is there a place i messed up?
I see what you’re trying to get at. If you’re trying to express how the load decreases linearly from a certain point, like from point 2, we should rather go step by step.
If the load decreases starting from point 2, and you’re using the distances, you would subtract from the total to find how far along the section you are. For a load decreasing over a section, the general form of the equation would be
q(z) = (starting load) ( 1 - z - start of section / length of section)
and again, the 1 - is separated from the division. If you’re trying to express how the load decreases over the third section L3 = 0.6 m, and you are decreasing from point 2, where z = 6, your equation would look like
q(z) = starting load ( 1 - z - 6 / 0.6)
Again the 1 - is seperate from the division.
Let’s break down the expression. 0.6 looks like you might be referring to distances, but remember that in the equation for the load, the subtraction should involve the position z and the starting point of the section. The “2” seems to be used twice, which could confuse some things. If you are referring to the length of the section, that should be 0.6 and not 2. Let’s come back to the equation,
q(z) = starting load ( 1 - z - 6 / 0.6 )
Where again, the 1 - is still separated from the division. The equation for a linear decrease over the third section should involve z and the section length, which again, is 0.6 meters, not 2.
If you are referring to the length L3 = 0.6, that would be the term you divide by, and not divide by 2.
honest lynx
With which part?
cunning prism
first off the divide by two isnt that always 2
beacuse its a trianlge and not square or rectangle
and where is the 6 coming from
and why is the z not 2 when we start from point 2
honest lynx
and why is the z not 2 when we start from point 2
Ah, ok. The divide by 2 you’re thinking of is used when calculating the force from a triangle load and not when writing the equation for the load distribution.
The number 6, or any other z, comes from the position along the beam where point 2 is located. The correct distance is
L1 = 3 m
L2 = 3 m
L3 = 0.6 m
Let’s make sure we are on the right track. Point 1 is where the first section L1 begins. At this point, z = 0 m.
Point 3 is the end of section L1, and section L2 starts. Since L1 = 3 m, point 3 is at z = 3 m.
Point 2 is where section L2 ends, and section L3 starts. Since L1 + L2 = 3 + 3 = 6 m, point 2 is at z = 6 m.
At the end of the beam is where the beam ends after section L3. Since L1 + L2 + L3 = 3 + 3 + 0.6 = 6.6 m, the end of the beam is z = 6.6 m.
Anyways, z is the position along the beam, so it corresponds to a coordinate, not the label of the points, like point 1 or point 2. If point 2 is at z = 6, then you use z = 6 in this equation. If point 2 is at z = 2, then you would use z = 2.
cunning prism
Ohhhhh
honest lynx
Yesss, I think you understand now?
cunning prism
[6-\frac{0,6-6}{2}]
cold dustBOT
Henriette
cunning prism
Yeah this is How it would be
cunning prism
Yesss, I think you understand now?
Would this be it for my task
cunning prism
@verbal verge if you have time to look sometimes it would be amazing
verbal verge
What can I help with ?
formal kayak
cunning prism
What can I help with ?
Basicly after all the explanation i can still not find the equation and i dont know what i am doing wrong cause i did think i got it But i didnt
cunning prism
I dont know honeslty
If i knew i would tell you haha But i am so so so confused
But i am guessing it might be kN/m
formal kayak
well they're asking for the distributed load in terms of Z
the distributed load can be quickly calculated by the F = mass x length formula
formal kayak
the formula is always mass x length to be precise
cunning prism
Yeah But cant have that when its not a rectangel
Its a triangle
That goes from 12kN/m to 0
formal kayak
i don't know where you took those numbers but yes, it goes from some number M to some smaller number M0 over the length l2
formal kayak
if you say 12kN/m to 0, then that must mean the load applied
cunning prism
Yes it is
formal kayak
but this only makes sense if the beam is supported only on the left end
formal kayak
engineering course? 
cunning prism
Yeah
But its in the math subject
Like calculus
But its mixed with mechnaics topics and we dont have that before next semester and no one is able to help me. Like the math help we have here is all clueless. Beacuse they Are doing mechatronics and data and
And chatgpt is as clueless as me
And other random students trying to help me doesnt know either
verbal verge
I am confused because I backread and everything is expressed with respect to x
Not z
cunning prism
I am confused because I backread and everything is expressed with respect to x
it is supposed to be with respect to x
verbal verge
Then it seems to me that you have a function graph and you just want said function
No?
cunning prism
no i want the mathmethial equation
verbal verge
I mean you want it in the form q(x) = function of x
And the function is already drawn on your figure
verbal verge
The load distribution is drawn on the figure
cunning prism
yeah
but thats not what i am asking about
i need to find a mathematihal equation
verbal verge
Oh okay, my bad, I thought it was
But then I don't understand what kind of equation you are looking for
cunning prism
i need to figure out the equation so i know how much load is gonna be on the beam
verbal verge
It says exactly that you want an equation to express q(x)
verbal verge
But q(x) is drawn on the figure?
As I said before
So I am confused about your requirements
If it's not just writing what q(x) is
verbal verge
Isn't q(x) the load?
cunning prism
yeah i guess
so basicly i know that to find the load for l1 it is 12kn/m * 3 m
wich is 36
but idk what the other one is for the triangle
verbal verge
For any x in [0,l1], q(x) = q_0
cunning prism
12kn/m * 3 m / 2 is what i though the triangle was
verbal verge
You can try to fit an affine function
cunning prism
affine?
verbal verge
For any x in [l1, l2], q(x) = a(x - l2) + b
So you have to find the correct a and b
So that border conditions are fulfilled
That is:
q(l1)= q_0
q(l2) = 0
cunning prism
i dont get it
cunning prism
yes
verbal verge
It shows a segment that is not horizontal right? Between l1 and l2
Or rather between l1 and l1 + l2
cunning prism
yup
cunning prism
idk what that is
verbal verge
In the form ax+b
cunning prism
oh yeah
verbal verge
So you just need to find the right a and b
So that it matches the borders
That is: q(l1) = q_0 and q(l1+l2) = 0
That is a system of two equations, with two unknowns a and b
You can solve it
cunning prism
why 0
cunning prism
no
at the begining of l2 its 12 kn per meter and it goes to 0 by the end of l2
idk why you plus l1 and l2
verbal verge
Because actually lengths are not cumulative
l2 is just the length of this chunk
But the x coordinate at the end is l1 + l2
cunning prism
yeah at the end
its 6
can you please use numbers i dont understand the math language
verbal verge
I don't know them tho
verbal verge
Yes, then l1 + l2 is 6
cunning prism
adn q0 is 12kn per meter
verbal verge
So for x from 3 to 6, you have an affine function to fit
cunning prism
why can i not just take like q0 * x/ 2
cunning prism
hm
verbal verge
I'm sorry, I need to leave, it's time for me to eat
But you can try my method I mentionned before
You know q(3) and q(6), so you need to find a and b to make an affine function
cunning prism
ok
honest lynx
@cunning prism sorry for the late reply.
honest lynx
Yeah this is How it would be
I see what you tried to do, but it seems slightly incorrect. This doesn’t really follow the format we need for a distributed load. The value 0.6 should actually be the length of the section, not subtracted by 6. There would finally be no division by 2 here unless if we are dealing with areas, certainly not in this case though. This is how you will write it
The distributed load decreases as z moves from 6 to 6.6.
At z = 6, the load is at its maximum.
At z = 6.6, the load reaches 0.
honest lynx
ok so the 1 is always a 1?
No, it’s not always a 1. It’s representing the starting point of the distributed load in the segment.
honest lynx
whats the z?
Z represents the distance along the beam from the start of the beam, usually from z = 0. For example, at z = 0, your at the start of the beam. At z = 3, your 3 meters from the start of the beam, which would be the end of L1. Moreover, you use z to show how the load changes as you move along the beam.
honest lynx
Would this be it for my task
Looking back to your total summary, again, your correct at L1 and L3, but it’s just always the L2 that’s incorrect.
cunning prism
yeah i am sliglty confused about the l2
honest lynx
I’ll talk about L2. Listen up my fellow student/madam.
For L2, the equation isn’t right because you’re trying to calculate the total force of from a triangular load, but your setup doesn’t match the correct expression for the linearly decreasing load, and we need to adjust it. The total resultant force for a triangular load should be
Resultant force = 1/2 x base x height
Right here, the base is L2 = 3m, and height/load intensity is q0 = 12kN/m.
Finally, the correct force for L2 should be
L2 = 1/2 x 12kN/m x 3m = 18kN/m
This now means that the total load over L2 is 18kN/m, not 36kN/m
So basically you missed out on halving your other answer (36kN/m)
cunning prism
yeah i have been realising all day that it should be 18 thats why i was so sure i was wrong
but i am confused why it is not [\frac{12kN/m * 3m}{2} ]
cold dustBOT
Henriette
honest lynx
but i am confused why it is not \[\frac{12kN/m * 3m}{2} \]
Because this approach would give you the total resultant force of the triangular distributed load, which is correct for calculating the resultant load on the beam.
cunning prism
but its giving me the correct answer
and idk what a resultant force is tbh
we havent had about force at all in class
honest lynx
I’ll tell you about the resultant force in a bit.
cunning prism
ok thank you
honest lynx
**Henriette**
I see the proper equation now. This formula gives the total force from a triangular distributed load, which is the area of a triangle representing the load over the beams length. However this isn’t the same as describing the distributed load function q(z) at any given point along the beam. Again, I’ve told you that the division by 2 is used to calculate the total force for the triangle load. The distributed load function q(z) is a line equation, which doesn’t require dividing by 2 because it’s about how the load changes at each point along the beam, not the total force.
The equation for this would be this.
cunning prism
but this is just for the l2 segment
and like the equation contains like 5 things
we have q0 = 12kN/m
how far out on the beam is the load starting to decrease = 3m from begining
and the starting point with the segment number = 2
and the length of the decreasin erea = 3
right?
honest lynx
but this is just for the l2 segment
Yes, exactly. For the L2 segment, where the load decreases linearly), the equation considers key factors. To confirm the components again, q0 = 12kN/m
This is the maximum load at the beginning of the L2 segment, right after L1. The load starts decreasing from 3 meters, which is the end of L1 segment. This distance is measured from the start of the beam, from point 0 to point 3. The starting point of the decreasing load is at the beginning of L2, so the segment number you’re referring to is the second segment (L2). The length of L2 is 3 meters, which is the range over which the load decreases from 12kN/m to 0kN/m. So, put into clear context, the load decreases over L2, which is 3 meters long, from 12kN/m to 0kN/m. Therefore, the linear decrease equation for the load along L2 is, again
If we reversal-simplify this:
• 12 would be q0
• the 3 on top, next to ‘z -‘ would be z(start)
cunning prism
ohh they make it so difficult with all the 3 haha
honest lynx
Oh and the 3 on the bottom would be L2
honest lynx
the 1 is......
Represents the full load at the start of the segment where the load begins to decrease
I hope you understand EVERYTHING that has been said
(Hopefully)
cunning prism
i am gonna have to make a summary back to you so we can see that we agree haha
i am so so sorry for being stupid
honest lynx
There is no problem at all
And sure, you can summarise it back to me like I’m a teacher.
I won’t be able to respond right now. I’ll respond tomorrow asap, so remind me.
Oh and also remind to explain to you what a resultant force is.
cunning prism
thats fine before you go
what is the z supposed to be
wich number do i replace it with
honest lynx
what is the z supposed to be
It represents the position along the beam. It’s the distance from the starting point of the entire beam to the point you are evaluating with the L2 section. (Where the load decreases).
Z - z(start) tells you how far you are into the decreasing load section L2.
The number you replace it with, when you’re calculating the distributed load q(z) for L2 section, you replace z with the actual position along the beam that you’re interested in. For example, if you are interested in a point at 4 meters (just an example btw) you would use z = 4 meters.
cunning prism
so for me it would be 6
or 3
like 6 is where it stops decreasing and 3 is where it stops
honest lynx
like 6 is where it stops decreasing and 3 is where it stops
Yup. As z increases from 3 to 6, the load q(z) decreases linearly from 12kN/m to 0kN/m.
cunning prism
ok soo now i got it i think cause when i put z as 6 i do get 0 on the calculator and when i put 3 i do get 12. and when i chek for 5 meters out on the beam from the begining i do get 4 so i can choose whatever point i want and i can find the load that is exactly there
and if it were to be 18kn/m to 0 over like 5 meter i would but in the same segment and l1 is the same it would look like this ( writing down and sending picture soon)
honest lynx
ok soo now i got it i think cause when i put z as 6 i do get 0 on the calculator...
Exactly!
honest lynx
You were really close, but let me clarify a bit. The equation you should use for the L2 section is based on the beam setup that we discussed earlier. Here’s the correct general equation.
cunning prism
yeah this was if the l2 was changed to be 5 meter long and the weight was changed to 18
but i got that
honest lynx
yeah this was if the l2 was changed to be 5 meter long and the weight was change...
yup.
tacit pumiceBOT
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honest lynx
is that all?
cunning prism
i think so
honest lynx
hey wait
cunning prism
oki
cunning prism
i can wait with closing til you explained that
but still thanks for this
you should have gotten like 10000 more rep points
honest lynx
it has been my pleasure being your teacher.
cunning prism
for this patience
litterlay i am so so gratefull
and thanks for dealing with me cause i am not the smartest
honest lynx
thats okay!
not everyone here is the smartest.
but anyways, lets talk about a resultant force.
cunning prism
we can do it tomorow cause its 10 pm
honest lynx
ah okay.
cunning prism
and i have been at school from 8 am and worked since that
but you can explain and i will see to oroow when i wake up
honest lynx
alright, no problem, i still have some time.
basically, a resultant force is the single force that represents the combined effect of all of the individual forces acting on an object. it simplifies the analysis of forces by reducing multiple forces into one equivalent force. a resultant force can be used in different subjects and points, but if we are talking about mathematical calculations, for forces acting in two dimensions, eg., horizontal and vertical, you can calculate the resultant force using the Pythagorean thorem if the forces are perpendicular, like this
where Fx and Fy are the components of the forces in the horizontal and vertical directions. The concept of the resultant force is crucial in physics and any other subject where multiple forces are acting. It can help determine whether an object with accelerate, remain stationary, or change its motion. For example (in physics), if you have two forces acting on an object,
Force A: 10 N to the right
Force B: 4 N to the left
the resultant force Fresultant would be,
Fresultant = 10N - 4N = 6N (to the right)
if you have two perpendicular forces,
Force A: 3 N upward
Force B: 4 N to the right
the resultant force can be calculated as,
the direction can be found using trigonometry e.g., tangent function, but you dont need to know this unless if you are studying physics.
cunning prism
oh i think this make sense
honest lynx
oh i think this make sense
if your'e certain that we are finished with this thread, you can close it now.
honest lynx
oooh nice
cunning prism
yes so thank you @honest lynx
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cunning prism
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