## Determination of bending moment and shear force

**Determination of bending moment and shear force
**

For this IS 456-2000 permits use of any one of the following two methods:

(a) The Direct Design Method

(b) The Equivalent Frame Method

**The Direct Design Method**

This method has the limitation that it can be used only if the following conditions are fulfilled:

(a) There shall be minimum of three continuous spans in each directions.

(b) The panels shall be rectangular and the ratio of the longer span to the shorter span within a panel shall not be greater than 2.

(c) The successive span length in each direction shall not differ by more than one-third of longer span.

(d) The design live load shall not exceed three times the design dead load.

(e) The end span must be shorter but not greater than the interior span.

(f) It shall be permissible to offset columns a maximum of 10 percent of the span in the direction of the offset not withstanding the provision in (b).

**Total Design Moment**

The absolute sum of the positive and negative moment in each direction is given by

In taking the values of L_{n}, L_{1} and L_{2}, the following clauses are to be carefully noted:

(a) Circular supports shall be treated as square supports having the same area i.e., squares of size 0.886D.

(b) When the transverse span of the panel on either side of the centre line of support varies, L_{2} shall be taken as the average of the transverse spans. In Fig. it is given by

(c) When the span adjacent and parallel to an edge is being considered, the distance from the edge to the centre-line of the panel shall be substituted for L_{2}.

**Distribution of bending moment into -ive and ive moments**

The total design moment M0 in a panel is to be distributed into –ve moment and ve moment as specified below:

**In an interior span**

Negative Design Moment = 0.65 M_{0}

Positive Design Moment = 0.35 M_{0}

In an end span

Interior negative design moment

Positive design moment