Kennedy, Goodchild - Practical Yieldline Design

Practical Yield Line Design

3.1.3 Location of maximum midspan moments and points of contraflexure Table 3.2 presents expressions for the location of maximum midspan moments and points of contraflexure. The parameters s1 and s2, the location of the points of contraflexure, are needed when checking the extent of top steel in accordance with BS 8110 clause 3.2.2.1 condition 3 which states: “Resistance moment at any section should be at least 70% of  moment at that section obtained from an elastic maximum moments diagram covering all appropriate combinations of design ultimate load.” 

Table 3.2 Location of maximum midspan moments and points of contraflexure n (kN/m2 )

m'1 = i 1 m

i1

i1 =

i2

m

m'1 m

s1

s2 x1

x2

m'2 = i2 m

i 2 = m'2 m

L

x1 = L

s1 = L

1+i1 1+i1 + 1 +i2 1+ i1 −1 1 + i 1 + 1 + i2

x2 = L

s2 = L

1+ i2 1+i1 + 1 +i2 1+i2 −1 1+i1 + 1 +i2

Where 

x1, x2 s1, s2 L i1 , i2 m m′1 , m′2

are the distances to maximum span moment [m] are distances to points of contraflexure, i.e. points of zero moment [m] span [m] are ratios of support to midspan moments is the maximum midspan moment [kNm/m] are the support moments [kNm/m]

3.1.4 Pattern loading: modes of failure and curtailment of reinforcement It is important to check how far to project the support steel into lightly loaded bays to ensure that the ultimate design moments at the supports can develop. Tables 3.3 and 3.4 depict the different modes of f ailure that could occur in continuous slabs when adjacent bays are subject to pattern loading. In most cases, extending support steel 0.25L into the adjoining span will usually suffice. However, if the designer has any doubt, Tables 3.3 and 3.4 may be used to check  curtailment. If the curtailed length of top steel is less than the computed length ‘cL’ then the slab in this bay will fail by cracking at the top, just at the ends of the top reinforcement and it will not be possible for the yielding of the support steel, as assumed in the original design, to take place. If the curtailed length of top steel is equal or greater than the computed length ‘cL’ then the slab full support moment can develop.

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