This document describes the virtual work method for determining the design moment of a rectangular slab using yield line analysis. It states that the internal virtual work done by rotations along yield lines must equal the external virtual work done by applied loads. The internal energy, which is the moment multiplied by the rotation and length of the yield line, is set equal to the external energy, which is the area multiplied by the load and average distance moved. This results in an equation to calculate the design moment based on the slab geometry and applied load.

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
