Midspan Moment of a Continuous Beam 1

[deedee2007]

The support moments of a continuous beam can be obtained using Clapeyrons Three-Moment Equation or Moment Distribution by Hardy Cross or other methods available. The mid-span moment of a section spanning between two supports a & b with uniformly distributed load can also be estimated using the formula: M = Mab -(Ma+Mb)/2
where Mab is midspan moment treating section as simply supported (WL2/8)
Ma = support moment at a
Mb = support moment at b.
My question is how do we estimate the midspan moment of a section spanning between two supports carrying a point load.
Can anyone help me out please.

 

[csd72]

The method is basically the same as the udl except the maximum span moment is at the point load location.

The effect of the end moments depends on the location of the point load, at the middle it is the average but if it is one third along it will be (2Ma + Mb)/2.

Alternatively you can calculate the plastic moments.

Hope this helps

csd

 

[rb1957]

this is simple statics ...

solve the two spans as though they are simply supported,
calculate the redundant moment at the middle support,
react this moment at the supports (a couple betwen the two remote supports) and the balancing load at the center.

then method of cuts to calculate the moment mid-span

 

[shin25]

If you want to use moment distribution-

Calculate the end moments due to the point loads as if the span is fixed. Then distribut the moments at the joints and carry over......

 

[JAE]

Agree with the above, but I'd point out that continuous spans for floors and roofs must have patterned loading applied which will require multiple analyses of the spans.

This means you will have the following live load patterns:

All spans loaded
Odd spans loaded
Even spans loaded
Adjacent spans loaded (3 conditions):
1, 2, 4, 5, 7, 8
2, 3, 5, 6, 8,
1, 3, 4, 6, 7,

See IBC 2000, section 1607.10 and 1607.11.1

 

[COEngineeer]

Just open your old structural analysis book. There are many methods to solve it and moment distribution is one of them.. OR maybe it is save to assume none of the moment will be distributed to the outer span and call it fixed fixed span.

Never, but never question engineer's judgement

 

[deedee2007]

You are quite correct csd72. I tried the method using the maximum moment under the point load and it worked. The only observation I made is that if the load is one third along the section the midspan moment can be estimated by
M = Mab - (2Ma + Mb)/L and not Mab - (2Ma + Mb)/2.
Thanks anyway csd72. You've really helped in cracking a very stubborn nut.