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Yield line solved rectangular slab
1. L
L
W
M ?
How to determine Design moment for a
Rectangular slab using Yield lineAnalysis
2. Virtual work method
L
L
Work done by external load in undergoing small virtual displacement is equal to
the internal virtual work done in rotations along Yield line.
W
3. L
L
/ 2
L / 2
L
/ 2
Internal Energy = External Energy
Internal Energy = Moment * rotation * length of projected yield line
External Energy =Area * Load * Average moved distance for each right half slab
W
4. L
L
/ 2
L
/ 2
Internal Energy = Moment * rotation * length of projected yield line
/ 2
/ 2
L
2 / 2
tan
L
/ 2
L
2 2 / 2
small angle, tan
L
For
2 / 2
L
4
L
Internal Energy 4M
4
Internal Energy *
M * L
L
W
? ?
5. L
L
/ 2
L
/ 2
/ 2
L
W
External Energy =Area * Load * Average moved distance for each right half slab
2
External 2*[( * ) * ( ) * ( )]
2
Energy L
L W
6. L
L
/ 2
L
/ 2
/ 2
L
W
Internal Energy = External Energy
2
2* [( * ) * ( ) * ( )]
2
4M L
L W
2
8
M WL