| Abstract: |
5-1 Conclusions: -In this thesis, and depending upon an experimental and 3-D non-linear finite element analysis, the effective width of composite beams consisting of steel I-beam supporting a concrete slab cast above corrugated steel sheeting (with & without slab openings) was investigated. This study covered the case of interior (T-sections) and exterior (L-sections) beams. The effect of the different influencing parameters on the effective width such as slab rectangularity, boundary conditions (existence of secondary beams), case and type of loading, concrete slab thickness, span depth ratio, opening width and length, and opening vertical position were also studied.A comparison among the well-known Codes of Practice [AASHTO, Japanese, British, LRFD, ACI, AISC, Eurocode 4, and Egyptian] and the current study was carried out. Composite beam features (deflection, steel & concrete stress, the ultimate and plastic moment capacities) were calculated based on the effective width according to different codes of practice and that from current study, to declare the great role of the effective width in estimating the beam strength.Hereafter the main important conclusions are discussed and illustrated:-1- In general, It can be stated that the effective width values recorded were constant for all values of rectangularity ratio in spite of increasing of load level up to either steel beam reached yield stress or concrete cracks began to propagate (which is closer), then it began to decrease. In all cases an increase in effective width was observed as the plastic hinge formatted then the effective width decreased till failure due to total collapse in the concrete.2- For low values of slab rectangularity ratios the steel has higher effect on the effective width at different loading level till failure (since yield in the steel occurred first), while for high values of slab rectangularity ratios concrete plays the more influence role.3- The existence of secondary beams has approximately no effect on the variation of effective width with increasing in loading level for low values of slab rectangularity ratios, while for high values of slab rectangularity ratios the effect of secondary beams existence on effective width values was noticeable.4- Increasing the concrete thickness by 50 % resulted in decreasing the effective width fluctuation at the beam middle-third distance from 17.2 to 5.6%, and from 17 to 3.7 % in average for exterior and interior beams respectively for high values of slab rectangularity ratios. While for lower slab rectangularity ratios increasing the concrete thickness has small effect on the effective width fluctuation.5- Corrugated steel sheet geometry produce fluctuation in effective width values due to change in concrete thickness from hollow to solid sections, the minimum values were located over the solid section. This fluctuation decrease with decreasing the rectangularity ratio, at the middle-third distance of the beam the fluctuation was 3.7 to 17.2 % in average for slab rectangularity ratios ranged from 0.34 to 0.67 respectively.6- Applying mid-span concentrated load produce a drop in the effective width at the nearest hollow section. The difference between the two sections (hollow & solid) was approximately constant (regardless of slab rectangularity ratios) about 16.5, 30 % in average for exterior and interior beams respectively.7- Increasing slab rectangularity ratios from 0.34 to 0.67 resulted in decreasing the normalized designed effective width by 31and 40 % for exterior and interior beams respectively for models loaded by uniform load. While for mid-span concentrated load the percentage was 38 % for both exterior and interior beams.8- Absence of secondary beam, and increasing the concrete thickness has no noticeable effect on the normalized designed effective width for both exterior and interior beams at lower values of slab rectangularity ratios.9- For higher slab rectangularity ratios the normalized designed effective width decreased by 14.4 and 7% for exterior and interior beams respectively, in model without secondary beam compared to that with secondary beam.10- Case of loading has no noticeable effect on the normalized designed effective width for interior beam, the difference was only 3% for all values of slab rectangularity ratios, while for exterior beam this value varied between 9 to 5 % when slab rectangularity varied from 0.34 to 0.67.11- Increasing the concrete thickness by 50% increased the normalized designed effective width by 17.1 and 26.5% for exterior and interior beams respectively at slab rectangularity ratio of 0.67. This proved that increasing concrete thickness was more effective in increasing the normalized designed effective width for higher values of slab rectangularity ratios.12- The normalized designed effective width in model loaded by mid span concentrated load decreased about 30% when slab rectangularity increased from 0.34 to 0.67 compared with that loaded by uniform load.13- Decreasing the span depth ratio by 50% resulted in increasing the normalized designed effective width by 11.4,7% for exterior and interior beam respectively for higher slab rectangularity ratios.14- All considered Codes of Practice underestimate the effective width design values under all conditions (safe design). Except for models with lower slab rectangularity ratios loaded by mid-span concentrated load in which the Codes of Practice [AASHTO, LRFD, ACI, AISC, Eurocode 4, and Egyptian] overestimate the effective width value by difference of 5.5,10% for exterior and interior beam respectively, this gives unsafe design so these values have to be revised.15- In the range of study, the Codes of Practice [AASHTO, LRFD, ACI, AISC, Eurocode 4, and Egyptian] had identical values for the effective width.16- The lowest underestimated values (i.e. very conservative) for the Egyptian Code of Practice were about 50 and 54 % for exterior and interior beams respectively at higher slab rectangularity {for models with (tc/h %=85.7)}.17- Although span depth ratio () has no noticeable effect on the underestimation difference values for all codes of practice. Egyptian Code of Practice underestimation differences were approximately constant with various span depth ratios. The underestimation difference was 43 (at =7.1) to 38 % (at =14.2), for both exterior and interior beam respectively, at slab rectangularity ratio of 0.6.18- Secondary beam absence has no noticeable effect on the calculated deflection, steel and concrete stress, ultimate and plastic moment capacities.19- Difference between the proposed effective width values and those obtained from different codes of practice, affect mainly the concrete stress for all slab rectangularity, rather than steel stress and deflection. The increase in concrete stress was ranged from 17 to 52%, at slab rectangularity ranged from 0.34 to 0.67, for Egyptian Code of Practice.20- Using the effective width according to the Egyptian Code of Practice (by difference of 38% compared to the proposed effective width) at higher slab rectangularity, results in increasing the deflection, steel and concrete stress by about 7.5% , 3.6% and 52 % respectively, compared to that calculated by the proposed effective width values. On the other hand, decreasing the ultimate and plastic moment capacities by about 15 and 18.5% respectively, which represents a considerable gained factor of safety.21- As the slab rectangularity ratio increased the effect of slab opening existence on the effective width for exterior and interior beams decreased. Also as the opening length ratio increased the effect of opening existence on the normalized design value decreased.22- At lower slab rectangularity ratio (r=0.34), the normalized design value decreased by 31 to 52 % and from 17 to 28 % for exterior and interior beams as opening length ratio (r1) decrease from 0.44 to 0.07 respectively compared to theses without opening. However in higher slab rectangularity (r=0.67), these percentages increased from 12 to 30 % and from 3 to 5 % for exterior and interior beams respectively.23- Slab opening existence has no effect on the normalized design value for exterior beam in the bay without opening.24- Increasing the opening width ratio increase the effect of opening existence on the normalized design value. For exterior beam at lower slab rectangularity, the normalized design value decreased by 52 to 88 %, these percentages were 30 to 92 % in models with higher slab rectangularity (r=0.67), in the range of study. For interior beam the normalized design value decreased by 28 to 64 % & from 5 to 66 %, for lower and higher slab rectangularity (r=0.34 & 0.67) respectively in the range of study.25- In higher slab rectangularity, existence of opening in the slab zone carried by interior beam has no effect on the normalized design value for exterior beam, this conclusion is also valid otherwise.26- By moving the opening toward the beam, for exterior beam the normalized design value decreased by 14 to 88 % & from 0 to 91 %, for lower and higher slab rectangularity (r=0.34 & 0.67) respectively. While for interior beam the percentages were reduced by 10 to 58 % and from 0 to 55 %, for lower and higher slab rectangularity (r=0.34 & 0.67) respectively.27- Based on the previous experimental and numerical analysis and from the effective width view, if it is required to make a slab opening, it is recommended to locate the opening out of the slab zone carried by beam (or as far as possible from the beam), and locate the opening corners as far as from the middle third of the beam span.28- By using the effective width for slab rectangularity ratio of 0.67 according to the Egyptian code of practice and that from current study the steel section needed was I.P.E 140 and I.P.E 120 respectively, resulting in a reduction in the steel weight by about 20 % (which shows the economic side of accurate estimation of the effective width).29- A Computer program was developed to calculate the effective width values. The designer can very easily define his case following very straightforward questions to obtain the effective width values according to the current research and also according to all available Codes of Practice.5-2 Future Work: -From the present research, the need to study some other related problems arises. Further research is required to be carried out in the following topics.1) The effect of considering partial interaction design on the effective width.2) The effect of dynamic load on the effective width.3) The effective width for curved beams.
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