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Beams are made continuous over the supports to increase structural integrity. A continuous beam provides an alternate load path in the case of failure at a section. In regions with high seismic risk, continuous beams and frames are preferred in buildings and bridges. A continuous beam is a statically indeterminate structure.
The analysis of a continuous beam is illustrated to highlight the aspects stated earlier. The bending moment diagrams for the following load cases are shown schematically in the following figures.
IS:456 - 2000, Clause 22.4.1, recommends the placement of live load as follows.
1) LL in all the spans.
2) LL in adjacent spans of a support for the support moment. The effect of LL in the
alternate spans beyond is neglected.
3) LL in a span and in the alternate spans for the span moment.
Incorporation of Moment Due to ReactionsThe moment diagram due to the eccentricity of the prestressing force and neglecting the intermediate support is denoted as the M1 diagram. This diagram is obtained as M1 = Pe, where, P is the prestressing force (P0 at transfer and Pe at service) and e is the ,mnbveccentricity of the CGS with respect to CGC. Neglecting the variation of P along the length due to frictional losses, the value of M1 is proportional to e. Hence, the shape of the M1 diagram is similar to the cable profile.
Free body diagram of concrete11
Next, the moment diagram due to the prestressing force and including the effect of the intermediate support is denoted as the M2 diagram. This is obtained by structural analysis of the continuous beam subjected to the upward thrust. Since the profile of the tendon is parabolic in each span, the upward thrust is uniform and is given as wup = w = 8Pe/l. The downward thrust at the location of the central kink is not considered as it directly goes to the intermediate support. The hold down force at the intermediate support neglecting the downward thrust is 10wupl/8 = 10Pe/l. The downward forces at the ends are from the anchorages
The strain in the reinforcement is equal to the strain in the concrete at the same level, i.e. es = ec at same level
Compressive s-e relationship for concrete may be assumed to be any shape that results in an acceptable prediction of strength
.
Beams are made continuous over the supports to increase structural integrity. A continuous beam provides an alternate load path in the case of failure at a section. In regions with high seismic risk, continuous beams and frames are preferred in buildings and bridges. A continuous beam is a statically indeterminate structure.
The analysis of a continuous beam is illustrated to highlight the aspects stated earlier. The bending moment diagrams for the following load cases are shown schematically in the following figures.
IS:456 - 2000, Clause 22.4.1, recommends the placement of live load as follows.
1) LL in all the spans.
2) LL in adjacent spans of a support for the support moment. The effect of LL in the
alternate spans beyond is neglected.
3) LL in a span and in the alternate spans for the span moment.
Incorporation of Moment Due to ReactionsThe moment diagram due to the eccentricity of the prestressing force and neglecting the intermediate support is denoted as the M1 diagram. This diagram is obtained as M1 = Pe, where, P is the prestressing force (P0 at transfer and Pe at service) and e is the ,mnbveccentricity of the CGS with respect to CGC. Neglecting the variation of P along the length due to frictional losses, the value of M1 is proportional to e. Hence, the shape of the M1 diagram is similar to the cable profile.
Free body diagram of concrete11
Next, the moment diagram due to the prestressing force and including the effect of the intermediate support is denoted as the M2 diagram. This is obtained by structural analysis of the continuous beam subjected to the upward thrust. Since the profile of the tendon is parabolic in each span, the upward thrust is uniform and is given as wup = w = 8Pe/l. The downward thrust at the location of the central kink is not considered as it directly goes to the intermediate support. The hold down force at the intermediate support neglecting the downward thrust is 10wupl/8 = 10Pe/l. The downward forces at the ends are from the anchorages
The strain in the reinforcement is equal to the strain in the concrete at the same level, i.e. es = ec at same level
Compressive s-e relationship for concrete may be assumed to be any shape that results in an acceptable prediction of strength
.
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