396 Report S.A.A. Advancement of Science. 



Deflection. 



As a rule bent iron reinforcements do not suffice, as the load 

 can change its position, thereby causing a change of the moments. 

 With continual ceilings we have a positive and a negative line of 

 maximum moments, according to which the reinforcement has to be 

 selected. Frequently a reinforcement running right through the 

 upper part of the plate is necessitated, especially if a short and 

 wide span are interchanging. Reinforced ceiling constructions have 

 arrived at such a pitch that it is impossible to refer to them in detail ; 

 there are close on 300 different methods of construction in existence, 

 and nearly every week a new system appears, which, however, in 

 most cases does not show any material improvement. "Different 

 ceiling systems have the technical fault, that above the supports the 

 reinforcement of the ceilings are placed in the lower part, and not 

 in the upper part of the plate as required by calculation. A progress 

 is noticeable in connection with those ceiling constructions, in which 

 the distance between the tensile and compressive zone is made as 

 great as possible, without, however, considerably increasing the dead 

 weight of the ceilings. This aim can be obtained through groins ; 

 so we then obtain groined ceilings consisting of interlocked T girders 

 of concrete, with reinforcement in the lower part of the groins. If 

 these reinforced groins are set apart in greater intervals, which 

 naturally necessitates a stronger construction ; the upper part forming 

 the compressive zone, should be reinforced as a plain concrete plate, 

 fixed between the groins, according to the theory just mentioned. 

 Whereby we obtain a groined ceiling construction in which the 

 ceilings with the reinforced concrete form a T profile. From a 

 theoretical point of view a plate strengthened by groins offers a more 

 economical n^ethod of using the materials than a plate of a constant 

 thickness. Up to a certain span, however, the greater cost for the 

 centering of the groins will compensate for the saving of material, 

 so that the groined ceilings can only be constructed with advantage 

 with a span of 10-12 feet or over. 



In the groined ceilings construction, the ceilings always statically 

 co-operate to a certain extent with the groin. As, however, the 

 bending moments are negative as in the case with fixed girders or 

 with unsupported girders running right through, and thus again the 

 tensile strength of the concrete is not taken into consideration, so 

 the calculation will be found to be the same as if the ceilings were 

 not in existence, that means that you have to proceed the same way 

 shown in the foregoing for the rectangular cross-section, with 

 this difference, however, that the tension zone with the reinforce- 

 ment is to be looked for in the upper part, while the compressive 

 zone acts in the lower part of the beam. Assuming that the rein- 

 forcement of the girder is evenly distributed on the operative width 

 of the plate, then the circulation can also be made with positive 

 bending moments for the rectangular cross-section if the neutral 

 axis lies within the ceilfng plate, or lies horizontally with the lower 

 part of the plate. 



