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# Deflection Equation for Composite Beam with Moment Connections

## Deflection Equation for Composite Beam with Moment Connections

(OP)
I need some help with a composite beam that has moment connections.  The examples in the ASD manual calculate deflection of a composite section as ML^2/161I, but their example follows a beam with a pinned connection.

Do the steel beam connections themselves play a part in the derivation of this deflection equation?  And if they do, how can I find/derive the equation that takes into account a fixed connection as opposed to pinned?

Any help would be great.

Thanks-
P333

### RE: Deflection Equation for Composite Beam with Moment Connections

You are describing an indeterminate structure. Time to dust off the old structural analysis books.

For a single member, moment-area is probably straightforward.

### RE: Deflection Equation for Composite Beam with Moment Connections

For an approximate solution, figure that a prismatic beam with fixed ends deflects around 20-25% of a beam with pinned ends.  But a composite beam with moment connections can really get complicated, as the composite moment of inertia will vary depending on whether the beam has positive or negative moment.  The negative bending moment of inertia will vary depending on whether the concrete is cracked or not, and on how much longitudinal slab reinforcing contributes to the section.

### RE: Deflection Equation for Composite Beam with Moment Connections

Is the slab part of the continuity, or is only the steel beam connected with moment connections, while the slab is disconnected to the support and only composite to the beam at this point?

### RE: Deflection Equation for Composite Beam with Moment Connections

(OP)
Thanks, meicz, I knew this one was going to be over my head.

PanamaStrEng: Only the steel beam is connected to columns with moment connections, and the slab is only composite with the beam.

Thanks!

### RE: Deflection Equation for Composite Beam with Moment Connections

I have seen a method that engages the tensile capacity of reinforcement placed in the concrete slab but this is generally only applicable to spread moments between the beams, transfer to the columns is more complicated.

### RE: Deflection Equation for Composite Beam with Moment Connections

Even considering equations 32 or 33 in the AISC manual, the solution is difficult due to the varying E and I along the length of the composite member.

I agree that for a reliable solution, a computer analysis is best here, breaking the span up into segments of appropriate E and I values

Mike McCann
MMC Engineering

### RE: Deflection Equation for Composite Beam with Moment Connections

It depends on how accurate you want to get with this of course. You can use moment area method with taking into account the inertia change if it happens that the concrete is cracked.

I have done this a couple of times before with concrete beams, you can use moment area to find deflections prior to cracking, at cracking, at yield, and at ultimate by plugging in the inertia changes along the beam at the affected locations then using moment area. Or you can do it with a computer program.

If it is a new beam, what I would do is design it to satisfy gravity deflection requirements using a pin-pin assumption and go home.

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