How to combine lateral wind load into the EQU equation? Eurocode 2 4

[Pretty Girl7]

I was checking the load combinations and then was trying to check for EQU. (Trying to learn how to do it in real-life situation)

My aim was to find out the loads acting on the beam and find the forces. Feed the forces into EQU equation stated below. Then feed the forces into bending moment equations to design the r/f needed etc.

The equation is from: clause 6.4.3.2, page 47, Eurocode 0.

I did the calculation to find the loads as below, but I don't know where to place the wind load in the equation as it's lateral load. I don't even know if the above equilibrium equation is supposed to have wind loads as well.

combination 1: (Self weight) + (1.5 x PL1) + (1.5 x 0.7 x PL2) + WIND LOAD

Ed = (1.35 x (2 kN/m x 6)) + (1.5 x 15 kN) + (1.5 x 0.7 x 20 kN) + WIND LOAD
Ed = 16.2 kN + 22.5 kN + 21 kN + WIND LOAD
Ed = 61.95 kN + WIND LOAD

Then I calculated total moments, but since I don't know where to put "wind load" in above equation, I didn't include it.
Total moments (MEd) = (Design load x length) / 8 + (Design load x length) / 4
= "(16.2kN x 6 m) / 8" + "(22.5kN x 6 m) / 4" + "(21kN x 6 m) / 4"
= 9 kN + 33.75 kN + 31.5 kN
= 77.40 kNm

I have mainly two questions.
1. How to include lateral wind load into that equation.
2. Is the calculation correct if we consider the wind-load didn't exist.

 

[centondollar]

1. You have drawn the wind load as an axial force. The problem includes coupling of compression and bending, which is not solvable by superposition. The effect of combined axial load and bending can be solved with closed-form solutions for specific cases, with a p-delta approach (geometric stiffness matrix to reduce beam bending stiffness and in that way approximate the axial-bending coupling) or with a full geometrically non-linear analysis which coupled axial and bending response through assumed beam kinematics.

The short answer is that you don't include the axial force in the equation for bending-only response. Instead, you must solve for the combined effect by using more complicated structural analysis than what you have presented.

2. Is there building framing or something else picking up wind load and transferring it into the beam as an axial load? I did not check your calculations in detail (you forgot one "L" in the "qL^2/8" formula for mid-span bending moment of a simply supported beam with uniform load), but you should not ignore wind if it acts on the structure.

 

[kostast88]

Wind is a variable action. Just like live load.

You treat it once as a "main" variable action γQ1,Qk,1 and the rest live loads as secondary (1.5x0.7)
Then you treat it as a secondary action. The factor ψ0 will come from the relevant tables of Eurocode according to your case.

This is the rule regardless of the problem. I believe your figure is indicative.

2. Wind load does exist, is given and is resisted by your supports. The sketch doesn't show supports but I assume this is simply supported = pin/roller so the pin will resist the wind load.

I see only upwards arrows in the supports. If you have no horizontal restraint then the system is unstable (a mechanism).

Wind load here doesn't generate any moment.

 

[ThomasH]

@Pretty Girl7
I think I asked you this in a previous post but I will try again. What is the purpose of all there questions regarding how to use the Eurocode? Is it some type of school assignment or what is it? The reason I ask is not to be rude but I think it would benefit if we knew a little about your basic knowledge on this subject.

Regarding your latest question, you ask about load combination EQU. If you start with the purpose of the combination I think it will be easier, and I have enclosed an extract from EN 1990 below.

This concerns the stability of a structure considered as a rigid body. In that case a typical approach for a "tower" is a low coefficient for stabilizing loads (like self-weight) and a high for overturning (like wind).

You mention an equation from clause 6.4.3.2 but EQU but in my Eurocode 1990 EQU is in clause 6.4.2. I find your questions a bit confusing . What is the purpose of all these questions? Trying to learn the Eurocode by asking questions on an Internet forum seems .......

 

[HTURKAK]

The sketch posted by OP is not clear for me, if the beam is part of portal frame or simply supported.. In this case , i prefered to post Summary of combined factors ( copy and paste from Structural Engineer’s Pocket Book, Eurocodes )..

Tim was so learned that he could name a
horse in nine languages: so ignorant that he bought a cow to ride on.
(BENJAMIN FRANKLIN )

 

[Pretty Girl7]

1. You have drawn the wind load as an axial force. The problem includes coupling of compression and bending, which is not solvable by superposition. The effect of combined axial load and bending can be solved with closed-form solutions for specific cases, with a p-delta approach (geometric stiffness matrix to reduce beam bending stiffness and in that way approximate the axial-bending coupling) or with a full geometrically non-linear analysis which coupled axial and bending response through assumed beam kinematics.

The short answer is that you don't include the axial force in the equation for bending-only response. Instead, you must solve for the combined effect by using more complicated structural analysis than what you have presented.

I can do a "sway analysis" and super impose it with "moment distribution" for wind to find actual combined effects of shear forces and bending moments. But what I don't understand is, where should I put those answers into that EQU equation? the equation seems to be accepting only seperate "axial" vertical loads for the combinations. And equation basically not asking combined effects as the purpose of the equation to see which "load combination" case causes more effects before we actually calculate the "combined effects of shear and moments" isn't it.

2. Is there building framing or something else picking up wind load and transferring it into the beam as an axial load? I did not check your calculations in detail (you forgot one "L" in the "qL^2/8" formula for mid-span bending moment of a simply supported beam with uniform load), but you should not ignore wind if it acts on the structure.

Yeah, I simplified it, the real structure would be a first floor of multi-story building, picking up wind on the wall surface as unfavourable manner. But that would make the reader more confused than now.

 

[Pretty Girl7]

Wind is a variable action. Just like live load.

You treat it once as a "main" variable action γQ1,Qk,1 and the rest live loads as secondary (1.5x0.7)
Then you treat it as a secondary action. The factor ψ0 will come from the relevant tables of Eurocode according to your case.

This is the rule regardless of the problem. I believe your figure is indicative.

2. Wind load does exist, is given and is resisted by your supports. The sketch doesn't show supports but I assume this is simply supported = pin/roller so the pin will resist the wind load.

I see only upwards arrows in the supports. If you have no horizontal restraint then the system is unstable (a mechanism).

Wind load here doesn't generate any moment.

So, you mean I can just combine the lateral and vertical loads together in the EQU equation? So it would add the wind load as either leading or accompanying variable as follows?

example combination 1: (1.5 x Self weight) + (1.5 x wind load) + (1.5 x concentrated load 1) + (1.5 x 0.7 x concentrated load 2)

example combination 2: (1.5 x Self weight) + (1.5 x concentrated load 1) + (1.5 x concentrated load 2) + (1.5 x 0.7 x wind load)

 

[Pretty Girl7]

You mention an equation from clause 6.4.3.2 but EQU but in my Eurocode 1990 EQU is in clause 6.4.2. I find your questions a bit confusing smile.

I assume you didn't understand the question. I was just asking in which way I can fit that 10kN windload into the equation, so I can see which combination makes most effect.
Further, Clause 6.4.3.2 contains the equation for EQU, STR and GEO as I understand. My question is mainly about that equation and how to feed windload into that as I was unsure how to do it as it's not vertical load, it's lateral.

 

[Pretty Girl7]

The sketch posted by OP is not clear for me, if the beam is part of portal frame or simply supported.. In this case , i prefered to post Summary of combined factors ( copy and paste from Structural Engineer’s Pocket Book, Eurocodes )..

I was just asking in which way I can fit that 10kN windload into the equation, so I can see which combination makes most effect. The windload got me confused as it's lateral, I was unsure if I can just chuck-in that 10kN load among other vertical loads.

By the way, thank you for the book reference "Structural Engineer’s Pocket Book, Eurocodes", although it's a pocket book, it will come in handy

 

[ThomasH]

I assume you didn't understand the question. I was just asking in which way I can fit that 10kN windload into the equation, so I can see which combination makes most effect.

In a way you are correct because I don't understand your question. If you are looking at stability it is EQU, if you are designing a beam it is STR (EC 1990 6.4.1). You mention bending moment and EQU, that is the reason I ask regarding the purpose of all your questions, and your signature says Civil/Environmental.

 

[Pretty Girl7]

In a way you are correct because I don't understand your question. If you are looking at stability it is EQU, if you are designing a beam it is STR (EC 1990 6.4.1). You mention bending moment and EQU, that is the reason I ask regarding the purpose of all your questions, and your signature says Civil/Environmental.

You basically created another confusion in my mind (in a good way). So if I wanna check for EQU, I need to put all the loads of 'entire multi-story building' into that one equation than just checking the beam individually? that means that one single equation would have like 100000 different loads (for entire multi-story building), and that equation would be long like the distance from earth to moon? and How many combinations that could have? gazzilion of combinations? or is there any other way to check EQU? How did the Engineers before ETabs or STAAD did it? What's the method in real-life situations.

 

[centondollar]

You are not "checking the beam" with EQU, but rather checking that the entire structure does not topple due to overturning. Alternatively, if the entire structure is just a beam (e.g., overhang beam), you use EQU to check if uplift occurs at supports.

If the contact between structure and ground is fully in tension, you have a global stability failure and failure of EQU criteria. Think of a gravity retaining wall overturning check.

 

[Pretty Girl7]

You are not "checking the beam" with EQU, but rather checking that the entire structure does not topple due to overturning. Alternatively, if the entire structure is just a beam (e.g., overhang beam), you use EQU to check if uplift occurs at supports.

If the contact between structure and ground is fully in tension, you have a global stability failure and failure of EQU criteria. Think of a gravity retaining wall overturning check.

The overturning check for the retaining wall is simple, you get the loads, find the lever arm, find the moments, multiply by safety factors and sum up all the moments and if it's positive, then it will not overturn.
But how that kinda process fit into this EQU equation for a multi-story building (clause 6.4.3.2, Eurocode 0)? because the EQU combinations are checked to find out which causes maximum effects before any moments are calculated. Now it's even more confusing.

So should I place all the 100000 loads acting on the entire building into the combination equation to find out which is the maximum loading case, and then proceed to sum up all the moments of the to check if it turns out to be positive? Because that's what we do to check overturning of the retaining walls.

 

[human909]

So should I place all the 100000 loads acting on the entire building into the combination equation to find out which is the maximum loading case, and then proceed to sum up all the moments of the to check if it turns out to be positive?

Yep pretty much, if you don't want to use critical thought. There are literally an infinite number combinations of possible of loads acting on the entire building.

But you only need a little bit of critical thought to reduce those infinite number down to the dozen or so critical cases.

You need to get your head around broader structural concepts. 6.4.3.2 The section you are referring to is a GENERAL format of combinations, it doesn't apply verbatim to all members. You need to be an engineer not an accountant.

 

[Pretty Girl7]

Yep pretty much, if you don't want to use critical thought. There are literally an infinite number combinations of possible of loads acting on the entire building.

But you only need a little bit of critical thought to reduce those infinite number down to the dozen or so critical cases.

You need to get your head around broader structural concepts. 6.4.3.2 The section you are referring to is a GENERAL format of combinations, it doesn't apply verbatim to all members. You need to be an engineer not an accountant.

Really? then enlighten me of how to do it exactly. I'm all ears

 

[HTURKAK]

You are looking for the load combinations to check for EQU. wright?

EQU is one of the Ultimate limit state is for checking the Loss of static equilibrium of the structure overturning,sliding, uplift ) or any part of it considered as a rigid body,or any part where the strength of construction materials or the ground is generally does not govern.

Assuming the subject beam is an element of a frame , the EQU combinations for the overall structure in this case ,

Ed1= 0.90 Gk,j + 1.5 Qk (wind) + 0.0* Qk (Imposed LL) FOR overturning,sliding, uplift..

Does this respond answers to your question? If not, provide a sketch of the total structure together with applicable loads..











Tim was so learned that he could name a
horse in nine languages: so ignorant that he bought a cow to ride on.
(BENJAMIN FRANKLIN )

 

[Pretty Girl7]

Think of a gravity retaining wall overturning check.

you only need a little bit of critical thought to reduce those infinite number down to the dozen or so critical cases

@Centondollar and @Human909,

I feel like I got what you meant by overturning an entire building and the reducing the number of critical cases. Are you saying to think it like a whole structure than individual forces acting in it.

For instance,

An entire face from ground to the roof top of a multi-story building wall getting a
1. maximum total windload of 2000 KN on the left side of the building etc --> variable Load 1
2. maximum total windload of 4000 KN on the right side of the building etc --> variable Load 2
3. Roof uplift 500 KN --> variable Load 3

In that manner I can think it as overturning a retaining wall and reduce the variables to less than dozen. Is that what you mean for the EQU check?

 

[Pretty Girl7]

You are looking for the load combinations to check for EQU. wright?

EQU is one of the Ultimate limit state is for checking the Loss of static equilibrium of the structure overturning,sliding, uplift ) or any part of it considered as a rigid body,or any part where the strength of construction materials or the ground is generally does not not govern.

Assuming the subject beam is an element of frame , the EQU combinations for the overall str.in this case ,

Ed1= 0.90 Gk,j + 1.5 Qk (wind) + 0.0* Qk (Imposed LL) FOR overturning,sliding, uplift..

Does this respond answers to your question? If not, provide a sketch of the total structure together with applicable loads..

It does, thank you

 

[Pretty Girl7]

Thank you all for providing answers, and even all of your criticism made me look at some aspects in a different viewing point to understand the "load combinations and checks" in a better way

 

[ThomasH]

Don't you have a more experienced colleague you can ask? If you had a sit-down with somebody that has some experience with load combinations in any code I think it would save you a lot of time.

I noticed that you consistently avoid questions regarding your background. The reason I asked, and I assume others also, is that it is easier to explaing if there is some kind of "common ground".