Midspan Moment of a Continuous Beam
Midspan Moment of a Continuous Beam
(OP)
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.
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.






RE: Midspan Moment of a Continuous Beam
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
RE: Midspan Moment of a Continuous Beam
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
RE: Midspan Moment of a Continuous Beam
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......
RE: Midspan Moment of a Continuous Beam
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
RE: Midspan Moment of a Continuous Beam
Never, but never question engineer's judgement
RE: Midspan Moment of a Continuous Beam
M = Mab - (2Ma + Mb)/L and not Mab - (2Ma + Mb)/2.
Thanks anyway csd72. You've really helped in cracking a very stubborn nut.