## analyse of multi bays braced frame

## analyse of multi bays braced frame

(OP)

I'd like to get the axial forces in a pinned supported 3 bays braced frame. The frame height is h=8m and the width of one bay is L=7 m.

There is only one point load of 1 kN applied on the top left corner.

I'm trying to get the reactions at the supports, but I don't know how to do that. I've also modelled the frame on SAP2000, and I don't quite understand the results (see image here):

The horizontal reactions make sense cause the sum is equal to the applied loading : -0.69+0.4+0.25+1.03 = 0.99 kN.

However, if I take the moment about the first support on the left for example, I get:

1*h-10.85*L-10.76*2L-6.88*3L = -363.07 kNm different from zero.

So I must be missing something here, and I'd really like to understand how to solve this by hand.

Thanks for your help.

There is only one point load of 1 kN applied on the top left corner.

I'm trying to get the reactions at the supports, but I don't know how to do that. I've also modelled the frame on SAP2000, and I don't quite understand the results (see image here):

The horizontal reactions make sense cause the sum is equal to the applied loading : -0.69+0.4+0.25+1.03 = 0.99 kN.

However, if I take the moment about the first support on the left for example, I get:

1*h-10.85*L-10.76*2L-6.88*3L = -363.07 kNm different from zero.

So I must be missing something here, and I'd really like to understand how to solve this by hand.

Thanks for your help.

## RE: analyse of multi bays braced frame

Considering a single inverted "V", with a load of 1/3, the horizontal reaction is 1/6 and the vertical reaction is (1/3)*8/7 = 8/21.

BA

## RE: analyse of multi bays braced frame

BA

## RE: analyse of multi bays braced frame

If this is pin jointed everywhere then I get Bay 1 as the only active member , in fact the only bars of interest are the first horizontal, and the first two diagonals.

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: analyse of multi bays braced frame

I agree that the first bay takes more than one third of the load and the middle bay takes more than the last bay, but without knowing the AE value of any of the members, we cannot tell how much each bay takes.

The key is the top horizontal member. If it is very stiff, the three bays share the load almost equally because they all deflect horizontally about the same amount. If it is very limber (soft, pliable, flexible), the first bay, as you suggested, takes the majority of the load.

With the given load, none of the vertical members takes any load. The top horizontal member takes a variable load with maximum of 1 kN at the left end and a minimum of zero at the right end.

BA

## RE: analyse of multi bays braced frame

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: analyse of multi bays braced frame

If axial deformation is included, the forces will change slightly.

BA

## RE: analyse of multi bays braced frame

Cheers

Greg Locock

New here? Try reading these, they might help FAQ731-376: Eng-Tips.com Forum Policies http://eng-tips.com/market.cfm?

## RE: analyse of multi bays braced frame

That is true, but the vertical reactions can't be evaluated without member properties because the structure is indeterminate, which means it can't be solved by statics alone.

BA

## RE: analyse of multi bays braced frame

Greg Locock

## RE: analyse of multi bays braced frame

Also, I'm not interested in deformations so far, only the axial forces in the members.

Anthony

## RE: analyse of multi bays braced frame

Okay, that allows the problem to be solved precisely.

The reactions are based on the assumption that the top horizontal member is sufficiently stiff so that each bay takes one third of the lateral load. In other words, I am neglecting the strain in the top horizontal member in order to make the structure statically determinate. It is a similar technique to neglecting axial strain when calculating the reactions of a rigid frame, using hand methods.

They would, but it is a secondary effect, or at least I believe it is. I have not gone through the calculation for the indeterminate structure. We can do that, if you wish.

In academia, a pin support means zero moment and zero translation. In practice, foundations do not behave as pin supports. Whether they are piles or footings, they rely on soil support, which is unpredictable. If three braced bays are required to resist the applied load, a structural engineer would likely assume that each bay was capable of resisting one third of the load. Alternatively, he could brace a single bay so that it was adequate on its own.

Unfortunately, you cannot find the axial forces in a statically indeterminate structure without ensuring that the deformations are compatible.

BA

## RE: analyse of multi bays braced frame

A horizontal member with axial force F and length L will strain FL/AE, in this case, 7F/AE.

With that information, it should be possible to write compatibility equations in order to determine all forces precisely.

BA

## RE: analyse of multi bays braced frame

The example you provided in your last reply, how does it work if I have several bays? And if I consider deformation, would that mean the vertical members would also take an axial load?

## RE: analyse of multi bays braced frame

Greg Locock

## RE: analyse of multi bays braced frame

Note: The last term in the fourth line is incorrect. It should read kX - c(2000 - 2X -Y). It was changed in my next post.

BA

## RE: analyse of multi bays braced frame

As expected, the force taken by each bay diminishes from left to right when the stiffness of the top member is included in the analysis. If the top member was increased in area, the difference would be less, but would still be evident. As it is, the first bay carries almost half the applied load.

Reactions may be readily calculated, but I have not included them.

BA

## RE: analyse of multi bays braced frame

Greg Locock

## RE: analyse of multi bays braced frame

Thanks for your reply BA, I just don't understand how you get the last line "horizontal deflection @TC", and how to you get c = 7/EA ?

## RE: analyse of multi bays braced frame

Strain in the top chord can be expressed as FL/AE where F is the axial force and L is the length of the member. For a typical interior panel, L = 7m, so strain = 7F/AE or cF where c = 7/AE. When F is compression, strain is negative.

2. Horizontal deflection at top chord

Let Points A, B and C be the middle of each of three bays.

Point A deflects kX.

Point B deflects kX - strain in AB = kX - c(1000 - X)

Point C deflects kX - strain in AB - strain in BC = kX - c(1000 - X) - c(1000 - X - Y)

There are two compatibility equations, one for Point B and one for Point C. These, combined with the equilibrium equation (X + Y + Z = 1000) provide the solution to the indeterminate structure, 3 equations for 3 unknowns.

BA

## RE: analyse of multi bays braced frame

## RE: analyse of multi bays braced frame

Just one further comment. It is always a good practice, after completing a complicated calculation, to sum the horizontal and vertical reactions and ensure they satisfy equilibrium, because it is easy to make an error along the way. When I checked your vertical reactions, at first I thought you were off by 300N, but I eventually realized I was reading your second reaction as 462.22 whereas you intended 162.22.

Cheers.

BA