CONCRETE STRUCTURES

	Two-Way Slab with Beams

		15'-40' span

		4" min.

		depth = slab perimeter/180

	Two-Way Flat Slab

		15'-40' span

		4" min.

		min. slab depth = span/36

		6"-12" typical

		drop panel min. depth = span/85

		drop panel min width = 0.4 span

	Two-Way Flat Plate

		15'-36' spans

		5" min.

		span/33

A flat plate floor with panels 20 by 25 ft 

is supported on 18 inches (45.7 cm) square columns. 

Interior exposure.

No edge beams are used.

From an investigation of a corner panel, 

what is the minimum required slab depth 

if deflection computations are not made? 

fy = 60 kips/sqin (413.7 MPa), and 

f'c = 3 kips/sqin (20.68 Mpa)

Long Side of Panel	Ll	= 20'-0"
Short Side of Panel	Ls	= 25'-0"
Columns		18" x 18"
			1'-6" x 1'-6"
No Edge Beam	
Interior Exposure
Steel			f'y = 60 kips/sqin
Concrete		f'c =   3 kips/sqin

Graphic Representation:
==================

For corner bay only!
Slab 	thickness
	reinforcement size
	reinforcement spacing
 

Step (#) by Step (#)
===============

 #1. Ln long	= Panel length - column width
		= 25'  -  1'-6" 
		= 23'-6"
		= 23.5"

#2. Ln short 	= Panel length - column width
		= 20' - 1'-6"
		= 18'-6"
		= 18.5'

#3. beta	 	= Ln long / Ln short
		= 23.5 ft  / 18.5 ft
		= 1.27

#4. alpha m 	= Ib / Is
		= I beam / I slab

#5.  No beam ===> Ib = 0		

#6. alpha m 	= Ib / Is
		= 0  / Is

#7. alpha m 	= 0

#8. if alpha m < 0.8 
      Increase slab thickness by 10% 
	multiply by * (1.1)  

#9. h min 	= ln [0.8 + fy/200,000] * (1.1)
		---------------------------------------------------
		36 + 5 beta [alpha m - 0.12 (1 + 1/beta]


		    #1                     given		#8
#10. hmin	= 23.5 * 12[0.8+60,000/200,000)]*1.1
		--------------------------------------------------
		36 + 5 * 1.27 [0 - 0.12 (1 + 1/1.27)
			  #3    #7		      #3

		= 282 * [0.8 + 0.3] * 1.1				
		--------------------------------------------------
		   36 + 6.35 [- 0.12 * (1 + 0.7874)]


		= 282 * [1.1] * 1.1						
		------------------------------------------------
  		 36 + 6.35 [ - 0.12 * 1.7874 ]


		= 282 * 1.21					
		--------------------------------------
   		36 + 6.35 * [ - 0.214]


		= 341.22			
		----------------------------
		36 - 1.362


		= 341.22	
		-----------------------------
		34.638


		= 9.85 inches	
		===========


#11.  But not less than

	h min = 	ln [0.8 + fy/200,000] * (1.1)
	   	----------------------------------------------	
			36 + 9 beta 


		=  23.5 * 12[0.8 + 60,000/200,000)]*1.1
		-----------------------------------------------------
			36 + 9 * 1.27

 		= 7.2 inches 
		==========


#12. Or more than

	h min 	= ln [0.8 + fy/200,000] * (1.1)
		----------------------------------------
   				36 


                    	     #1		given                   #8
		= 23.5 * 12[0.8 +60,000/200,000)]*1.1
		-------------------------------------------------------------
				36 

		= 9.48 inches
		===========

#13.      7.2" < h min < 9.48"
	#11	         #12	

#14.      9.85 > h min			
	DOES NOT CONTROL

#15.	9.48 inches
	==========
	controls

#16.	Table 1.1 Page 493
	Minimum thickness of slabs
	without interior beams

Given:
	fy = 60,000
	without drop panel
	exterior panel
	without edge beam

look-up from table
	h min	= ln /30
	h min 	= longer span / 30
		= 282/30
		= 9.4 inches
		===========

#17.	 9.48 inches governs
Answer	9.5" slab thickness