FOOTING

Footing -  A base (in or on the ground) that will support the structure. A masonry section, usually concrete, in a rectangular form wider than the bottom of the foundation wall or pier it supports. - The base or bottom of a foundation pier, wall, or column that is usually wider than the upper portion of the foundation. The added width at the bottom spreads the load over a wider area.

TYPES OF FOOTINGS Footing requirements are generally covered in the building code and sized in accordance with the bearing capacity of the soil and the weight of the building. In areas subject to seasonal frost, the bottom of the footing must be placed below the frost line to prevent damage to the footing and structure due to frost heave. Typical footing types include: spot footings continuous spread footing grade beam footing

Problem 1: A 150 mm wall is carrying a total load of 150 kN per meter length of wall. Design a wall footing using the following: fc’= 20 Mpa fs = 140 Mpa n = 9 R = 1.45 Mpa j = 0.878 v = 0.50 Mpa u = 2.2 Mpa Allowable soil pressure = 75 kPa

Solution: Consider 1m length of wall; Assume wt. of footing = 0.09(150) = 13.5 kN Total load = 150 + 13.5 = 163.5 kN Req’d. Area = 163.5 = 2.18 m² 75 L(1) = 2.18 Net soil pressure = 150 = 68.2 kN 2.2 m

Determine depth of footing: from bending M = 68.2 (1.025) (1.025) 2 M = 35.83 kN · m d = 157 mm

from shear V = 68.2 (1.025 – d) kN Use d = 160 mm v = V Total depth = 160 + 75 = 235 mm bd 0.40 = 68.2(1.025 – d) (1000) Check wt. of footing (1000) (d) (1000) wt. of footing = (2.2) (0.235) (1) (2.4) 5.865 = 1.025 – d = 12.2 kN < 13.5 kN d = 0.149 m d = 149 mm

A reinforcement; Deck bond stress: As = M fs jd Spacing = 314 (1000) = 172 mm 1822 As = 35. 83 (1000)² 140 (0.878) (160) = 20 mm bars 170 mm o.c. As = 1822 mm² Deck bond stress: u = V  jd V = 68.2 (1.025) = 69.9 kN  =  (20) (1000) = 370 mm 170 u = 69.9 (1000) = 1.34 MPa < 2.2 MPa (ok) 370 (0.878) (160)

temp. bars Ast = 0.0020 (2200) (235) Ast = 1034 mm² For 12 mm bars A =  (12) ² = 113 mm ² Use 10 – 12mm bars

Problem 2: Design a square footing for a spiral column having a diameter of 678 mm carrying an axial load of 1780 kN. Allow. soil bearing pressure = 240 kPa fc' = 17.5 MPa fs = 138 MPa n = 12 k = 0.406 j = 0.865 = 0.17 R = 1.38 u = 10.14 v = 0.09 D

Solution:   Assume wt. footing = 6% of 1780 wt. footing = 0.06 (1780) wt. footing = 106.8 Kn Total load = 1780 + 106.8 = 1886.8 kN Required area = 1886.8 = 7.86m² 240 L² = 7.86 L = 2.80 m Net upward soil pressure = 1780000 7.85 = 223899 N/ m² Try 2.82 x 2.82 A = 2.82 (2.82) Note: Change the round column into a square section  A = 7.95 m²

(678)² = D² D = 600 mm   M = 223899 (2.82) (1.11) (1.11) 2 d = 316 mm (Add 100- 200 mm approx.)   Try d = 490 mm

Check for beam shear:   V = q (c-d) L V = 223899 (1.11- 0.490) (2.82) V = 385151 N ν = 385151 2820 (490) ν = 0.28 MPa va = 0.09 va = 0.38 MPa > 0.28 (safe)

Check for Punching shear:   Vp = q [L² - (d+a)²] Vp = 223899 [(2.82)² - (1.09)²] Vp = 1514520 vp = Vp Ap Ap = 490 (1090) (4) Ap = 2136400 vp = 1514520 2136400 va = 0.17 vp = 0.709 MPa va = 0.71 MPa > 0.709 (safe)

(to compensate for bond stress) Compute the steel requirements: Check for Bond stress:  =  (28) (13)    = 1144 mm As = 6650 mm²   Using 28 mm Ø bars: (28)² n = 6650 n = 10.81 say 13 bars (to compensate for bond stress)

check wt. of footing:   Total depth = 490 + 28 (1.5) + 75 = 607 mm wt. = 0.607 (2.82) (2400) (9.81) (2.82) wt. = 113694 N check the area required: A = A = 7.89 m² < 7.95 m² (our trial area is bigger than the required area) V = 223899 (1.11) (2.82)   V = 694535 N u = 1.43 MPa ua = 1.51 MPa > 1.43 (safe)

Foundation – the interfacing element between the superstructure and the underlying soil or rock.   Foundation Engineering – art and science of applying engineering judgment and the principles of soil mechanics to solve the interfacing problem Retaining Structure – structure whose purpose is to retain a soil or other similar mass in a geometric shape other than occurring naturally under the influence of gravity S = total ultimate settlement S = Si + Sc + Ss Si = immediate settlement resulting from the constant volume distortion of the loaded soil mass Sc = consolidation settlement resulting from the time dependent flow of water from the loaded area under the influence of the load generated excess pore pressure which is itself dissipated by the flow Ss = secondary settlement or creep which is also the dependent but may occur at essentially constant effective stress

Typical Foundation Types are: Foundation for building (shallow/deep) Foundations for smoke stacks, radio and television towers, etc. (s or d) Foundations for port or Marine structures (maybe s or d, w/ extensive low or deep) Foundation elements support open cuts or retain earth masses or bridge abutments (retaining structures)

Problems encountered in foundation designs What constitutes satisfactory and tolerable settlements? How variable is the soil Profile, and has client seen willing to authorize an adequate exploration program? Can be the building be supported by the underlying soil on spread footing, mats, piles? What is the likehood of a lawsuit if the foundation does not perform adequately? Is money available for the foundation portion of the construction? What is the ability of the local construction force? What is the engineering ability of the foundation engineer?  

General Requirements of Foundations Depth must be adequate to avoid lateral expulsion of materials from beneath the foundation, particularly footing and mats. Depth must be below seasonal volume changes such as freezing and thawing or the zone of organic materials System must be safe against overturning, rotation, sliding, or soil rupture System must be safe due to harmful materials present in soil System should be adequate to sustain some changes be major in scope The foundation should be economical in terms of the method of installation Total earth movements and differential movements should be tolerable for the foundation element and or any superstructure elements

Soil Mechanics Engineering study of soil to obtain properties such as:   Engineering study of soil to obtain properties such as: Strength Parameters Compressibility Indexes Permeability Gravimetric – volumetric data (unit, weight, specific gravity, void ratio)    This makes possible engineering Predictions and estimates of: Bearing Capacity Settlements -amount -rate Earth Pressures Pore Pressures and Dewatering quantities The foundations engineer is concerned with the construction of some type of engineering structure of the earth great effort is required to separate the particles

Earth – composed of rock and soil   Rock – naturally occurring materials composed of mineral, particles so firmly bonded together that relatively Soil – naturally occurring materials minerals particles which are fairly readily separated into relatively small pieces and in which the mass may certain air, water, or organic materials in varying accounts Attenberg Limits – laboratory tests for arbitrary moisture contents to determine when the soil is on the verge of being viscious liquid (liquid limit) or nonplastic Plastic Index – water content beyond which no further reduction of mass, volume takes place with additional moisture loss Specific Gravity – may be determined in a laboratory test with moderate difficulty

Soil Classification Terms   Bedrock – rock its native location, usually extending greatly both horizontally and vertically Boulders – smaller pieces of materials which have broken away from bedrock (10-12 in) Gravel – common term used to describe pieces of rock from about 6 in. max. to less than ¼ in min. size Sand – mineral particles ranging size from 0.05 to 0.074 mm max to 0.002 to 0.006 mm Clay – mineral particles smaller than silt size

SPT N value Relative density 0-4 very loose 4-10 loose   SPT N value Relative density 0-4 very loose 4-10 loose 10-30 medium dense 30-50 dense 50 very dense