Problem

A column transfers a factored load of 700 kips to the 9-ft square spread footing shown in Figure, resulting in a factored uniform soil pressure of 8640 psf. Design the footing reinforcement using strut-and-tie methods. Material strengths are f′c = 4000 psi and fy = 60,000 psi. Because footings typically contain no shear reinforcement, your design should be based on unreinforced bottle-shaped struts.

FIGURE

Step-by-step solution

1. Step 1 of 1

   A column transfers a factored load of 700 kips to the 9-ft square spread footing shown in Fig. P10.5, resulting in a factored uniform soil pressure of 8640 psf. Design the footing reinforcement using strut-and-tie methods. Material strengths are f′c = 4000 psi and fy = 60,000 psi. Because footings typically contain no shear reinforcement, your design should be based on unreinforced bottle-shaped struts.

   Strut and Tie data
   βn = 0.8	C-C-T Note
   βs = 0.6	Bottle shaped strut with no shear reinforcement
   φ = 0.75
   width= 102 in

   material Data
   f′c=	4000 psi
   fy=	60 ksi

   Strut strength = 0.85 f′c × βs × φ
   fns =	1530 psi

   Loads = q × tributary area
   P1= 103.5 kip	4 Locations
   P0 = 90.6 kip	2 Locations

   	Geometry
   	h	b	L
   1	29	40.5	49.8
   2	29	24.5	38.0
   3	29	8.5	30.2

   	Strut Loads	Strut thickness = Load/(strut strength × width)
   1	155.7 kip	1.00 in
   2	135.5 kip	0.87 in
   3	107.8 kip	0.69 in

   All struts fit within the geometry

   	Tie Loads = horizontal component of strut load
   	1	126.6
   	2	87.4
   	3	30.3
   Total		244.3	kip  Tensile force at midspan

   As = 5.43 in2	n= 6.87 #8
   	As= 5.53 in2

   DESIGN

   Use

   7- #8 at 12 in each way

   Hook bars at end for anchorage