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# Second Moment Area of Moment Frame with Shear Truss

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## Second Moment Area of Moment Frame with Shear Truss

(OP)
Hi there,

I am trying to calculate the deflection of a moment frame made up with a shear truss.

Each bay is 3 metres, so total height is 12 metres. I am using a static horizontal load of 10000 N/m.

I am modelling it as a cantilever beam using stiffness 'K' as (8*E*I)/L^4

I need to find the second moment area of the structure. For the shear truss alone I get the correct deflection. In the literature I have found that the second moment of area is 0.9*(2*(A*1.5^2)). A is the cross-sectional area of the column, 1.5 is the distance in metres from the neutral axis. Using this I get the correct answer. However, when I add unbraced bays to each side I do not.

I guessed that the new second moment area of the total structure is 0.9*(2*(A*1.5^2)) + 2*(A*4.5^2), but I don't get the correct answer from this.

So, Could somebody please tell me what the second moment of area for this structure is, please?

Best wishes

### RE: Second Moment Area of Moment Frame with Shear Truss

It doesn't really have a "second moment of the area" in the strict sense. The drift at the top is a function of many input parameters, including the types of connections between all of those members.

You could use the program to compute the drift at the top and back-calculate an "effective second moment of the area."

For example, apply P = 50 kips laterally at the top, and calculate the drift, Delta. Then use Delta = PL^3 / 3EI to back out Ieff. That's the closet thing to what you're asking.

### RE: Second Moment Area of Moment Frame with Shear Truss

The usual approach to 2d truss analysis is a graphical method of great beauty. It superimposes the FBDs of each joint. The members themselves are not labelled, the spaces between them are. Sadly my google fu has failed to find the proper name for it.

Cheers

Greg Locock

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### RE: Second Moment Area of Moment Frame with Shear Truss

I remember those diagrams, fondly, from my undergraduate days in the late 1960s.  "Maxwell diagrams".

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