The flat slab structural system is commonly implemented in projects in Saudi Arabia due to the higher average labortomaterialcost ratio in the country. This system provides multiple structural, architectural, and construction advantages. The absence of internal beams in flat slabs allows for quick and straightforward construction and simple formwork installation
Research proved that Saudi Building Code (SBC304) and American Concrete Institute (ACI318) spantodepth ratio requirements for oneway solid slab design always result in relatively conservative slab thickness values which leads to increased material costs
The impact of span length on the unit cost of slabs has not been discussed comprehensively within the context of Saudi Arabia. The slab construction cost forms most of the reinforced concrete (RC) structural element’s costs
The paper conducts research through five steps prescribed in
Direct search approaches are usually utilized when solving issues when the objective function is not continuous and differentiable. In a stochastic or nonstochastic process, they primarily look at the objective function to find the optimum solution based on previous findings. It is frequently thought of as a general word for optimization algorithms that employ objective function values rather than gradients of objective functions. This definition of direct search fits many different methods used today. The study applied Pattern Search Methods (PSM), which fall under the category of direct search methods and iterative design approach to identify the optimum design characteristics and loading conditions to flat slab design
The study applied the Direct Design Method following the limitations and requirements of the Saudi Building Code (SBC) to generate






3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

3 
S1 
S2 
S3 
S4 








4 

4 

S5 
S6 
S7 
S8 
S9 







5 


S10 
S11 
S12 
S13 
S14 
S15 





6 



S16 
S17 
S18 
S19 
S20 
S21 
S22 



7 




S23 
S24 
S25 
S26 
S27 
S28 
S29 
S30 

3 
S31 
S32 
S33 
S34 








5 

4 

S35 
S36 
S37 
S38 
S39 







5 


S40 
S41 
S42 
S43 
S44 
S45 





6 



S46 
S47 
S48 
S49 
S50 
S51 
S52 



7 




S53 
S54 
S55 
S56 
S57 
S58 
S59 
S60 

3 
S61 
S62 
S63 
S64 








6 

4 

S65 
S66 
S67 
S68 
S69 







5 


S70 
S71 
S72 
S73 
S74 
S75 





6 



S76 
S77 
S78 
S79 
S80 
S81 
S82 



7 




S83 
S84 
S85 
S86 
S87 
S88 
S89 
S90 

3 
S91 
S92 
S93 
S94 








7 

4 

S95 
S96 
S97 
S98 
S99 







5 


S100 
S101 
S102 
S103 
S104 
S105 





6 



S106 
S107 
S108 
S109 
S110 
S111 
S112 



7 




S113 
S114 
S115 
S116 
S117 
S118 
S119 
S120 

3 
S121 
S122 
S123 
S124 








8 

4 

S125 
S126 
S127 
S128 
S129 







5 


S130 
S131 
S132 
S133 
S134 
S135 





6 



S136 
S137 
S138 
S139 
S140 
S141 
S142 



7 




S143 
S144 
S145 
S146 
S147 
S148 
S149 
S150 
The paper used iterative design, variable live load testing, and quantities and costs estimation techniques to generate material quantitates data for cost analysis. The design process included the use of spreadsheet software to carry on the iterative procedures of design and estimations. The program algorithm we coded shown in
Where:
This section prescribes the computing of the materials required quantities and minimum steel reinforcement after the determination of slab design characteristics. The following Tables show the quantities and cost data output from the spreadsheet for all slabs included in the study. Each table considers the slab design under certain live load conditions. The slabs have been divided into five categories based on live load. Each category is further divided into groups based on the short panel dimension. For instance, slab S25 falls in group 5 in category 1 (C1G5).
Live Load (LL.) (K.N./m2) 
Panel Short Direction (ly) (m) 

Panel Long Direction (lx) (m) 
Average Unit Cost for Load (SR.) 


3 
4 
5 
6 
7 
8 
9 
10 
11 
12 
13 
14 

4 
3 
81 
82 
88 
107 








140 

4 

83 
90 
108 
119 
138 







5 


92 
109 
120 
139 
151 
170 





6 



112 
123 
141 
153 
172 
184 
204 



7 




126 
143 
155 
173 
186 
205 
218 
238 

5 
3 
81 
82 
89 
108 








142 

4 

84 
91 
109 
121 
139 







5 


94 
111 
122 
141 
153 
172 





6 



113 
125 
143 
155 
174 
187 
206 



7 




129 
145 
157 
176 
189 
208 
221 
242 

6 
3 
81 
83 
91 
109 








144 

4 

85 
93 
110 
122 
141 







5 


96 
112 
124 
143 
155 
175 





6 



116 
127 
145 
157 
176 
189 
209 



7 




132 
148 
160 
179 
192 
211 
225 
245 

7 
3 
81 
84 
92 
110 








146 

4 

86 
94 
112 
124 
143 







5 


98 
114 
126 
145 
145 
177 





6 



118 
129 
147 
160 
179 
192 
212 



7 




135 
150 
163 
181 
195 
214 
228 
248 

8 
3 
82 
84 
93 
111 








149 

4 

87 
96 
113 
126 
145 







5 


100 
116 
128 
146 
160 
179 





6 



120 
132 
149 
162 
181 
195 
214 



7 




138 
153 
166 
184 
198 
217 
231 
251 

Average Unit Cost for Span (SR.) 
81 
84 
93 
112 
126 
144 
157 
176 
191 
210 
225 
245 
144 
The analysis results for slabs unit cost in category one under a live load of 4 kN/m^{2} ranges from 81 SR ($21.6) to 238 SR ($63.5), around three times increment. Slab S1 had the lowest cost, while S30 had the peak. Slabs S1, S5, S10, S16, and S23 had the lowest unit cost between slabs for each group within the same category, while S4, S9, S15, S22, and S30 costs were the greatest. The results show a proportional increase in unit cost with span length. Regarding the proportionate materials costs, steel reinforcement percentages from the total appear to increase with increment of span length while Formworks' share of cost decreases. Steel cost percentage varied from 42% to 56%, and formworks decreased from 21% to 7%, averaging 50%, and 13% for steel and forms, respectively. The span length seems to have little to no impact on the concrete share of costs, with a slight variance from 35% to 38% and an average of 36%. This could be detrimental for projects in regions with low availability of wood or steel and their respective costs. However, this is subject to the study of steel and wood base costs in any given region. Results related to category two slabs shows similarity to category one. Unit costs analysis was almost identical to the previous findings that S31, S35, S40, S46, and S53 had the lowest costs, while S34, S39, S45, S52, and S60 had the lowest unit costs. The unit costs varied from 81 SR ($21.6) to 242 SR ($64.5). The materials costs percentages for category two were also similar, with an average of 36% for concrete, 51% for steel, and 13% for forms. The results of category three follow a similar pattern to those of categories one and two. The shortest slab in each group had the lowest cost, while the longest had the greatest value. The material percentage costs also follow a similar form. This would continue with the results of categories four and five.
The analysis shows that the increase in slab length significantly multiplies the material costs, a pattern corresponds with findings in similar studies
Where Cu is the unit cost per one unit area of RC slab and x is span length.
Regarding the variable live load impact on slab cost, the study showed that live load increment increases slab material unit cost/m^{2} slightly.
Dimensions 
Live Load (kN/m^{2}) 
Increment% per 1 kN/m2 

Long 
Short 
4 
5 
6 
7 
8 

3 
3 
81 
81 
81 
81 
82 
0 
4 
4 
83 
84 
85 
86 
87 
1 
5 
5 
92 
94 
96 
98 
100 
2 
6 
6 
112 
113 
116 
118 
120 
2 
7 
7 
126 
129 
132 
135 
138 
2 
6 
3 
107 
108 
109 
110 
111 
1 
8 
4 
138 
139 
141 
143 
145 
1 
10 
5 
170 
172 
175 
177 
179 
1 
12 
6 
204 
206 
209 
212 
214 
1 
14 
7 
238 
242 
245 
248 
251 
1 
The reinforced concrete material's proportional costs vary for each studied case. In addition, the analysis showed that the proportionate cost of each of the three components is affected by the increment in span length.
The study investigated the impact of span length and live load increase on slab material cost. The study focused primarily on flat slab structures for projects implemented in Saudi Arabia. The study confirmed that increasing slab span considerably increases unit cost while the increase in live load minimally affects unit cost. Using the numerical procedure, we developed the mathematical model prescribed by Equation 2 to facilitate a relationship between span length and unit cost. The model can be implemented to allow a more accurate estimate of flat slab costs using span length only. This could be beneficial for early project estimates, especially in preliminary estimations before the completion of the design phase. The model would also enhance the application of value engineering principles through more accurate estimations and consideration of variable span designs. However, the model did not factor in the costs for other slab structural systems. Further study would improve the model or generate a novel one to consider solid slabs, ribbed slabs, or prestressed elements. In addition, further research would include prices for specific periods or any local region indexes to introduce time value and location local prices that affect the model.
The study results showed that a panel with a 1:1 lengthtowidth ratio seems more economical than panels with 2:1 dimension ratio; therefore, the authors recommend maintaining square dimensions as much as possible. Regarding live load testing, analysis revealed that panels with 2:1 ratio are less affected by live load increment than 1:1 ratio panel. This could be the subject of further study to confirm and conclude the theory. Since the study generally covered flat slab structures without considering building function, the authors recommend studying the optimal design with combination of live load and span impact simultaneously for specific building functions covering residential, commercial, health, educational, or administrative buildings.
The RC material costs are categorized into concrete, reinforcement steel, and formwork. Generally, the concrete cost would compose 36% of the total material cost. The reinforcement steel consumes the most significant portion of the RC material budget, representing 52% of the total costs. The formwork is a minor contributor, with only 12% of the total. Therefore, further studies regarding cost optimization should be more focused on reinforcement steel. However, our study only covered materials base costs and did not consider the labor, equipment, or project indirect costs, which would form the bases for further research. The effect of columns and the impact of other structural elements can also be explored.
The authors would like to thank the College of Engineering and Islamic Architecture and Deanship of Scientific Research at Umm AlQura University for supporting this work.
Data and calculations regarding each slab case are provided within supplementary materials Table S1.