bending moment induced in walls due to temp diffrential

huangyhg

bending moment induced in walls due to temp diffrential
i would like to know the members opinion on the bending moment induced in walls of a concrete silo used for storing hot materials like clinker and design approach to them.
aci 313 r gives a expression for bending moment induced in the wall, and suggests that circumferential steel be put on the outer face of the wall.this means that there will be tensile stresses generated on outer face and compressive stresses generated on inner face.
my interpretation of the effect of hot material inside the silo is the following:-
assuming that the temp of the outer fibres remains same as
that of outside.
the inner fibres will want to expand , but since they are constrained from movement, there will be compressive force produced in them.
the outer fibres will retain their axial dimensions and hence no stresses shall be produced in them.
the intermediate fibres will be in compressive state.
the section will resemble a prestressed section with triangular stress distribution and theoretically there wont be any need to provide steel to counter effects of temp diffrential.
i would like to know the flaw in my reasoning.
regards
sshinde
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the flaw originates with "the inner fibres will want to expand , but since they are constrained from movementfff">, there will be compressive force produced in them".
the inner fibres are not totally constrained from movement.  they are elastically restrained by the presence of the cooler parts of the wall further out from the heat source.  these cooler parts end up in a state of tension.  the tension stresses in the outer part of the wall exactly counter the compression forces in its inner part.  (simple statics tells you this must be so:  there can be no net hoop force in the wall because there is no radial pressure loading in the load case being considered.)
if it is assumed that the temperature varies linearly through the wall thickness, then the stressfff"> variation through the thickness will be exactly the same as if it had been induced by a pure bending moment.  but the strainfff"> variation will not.
see my answer to this thread: