2.2 STRUCTURAL ELEMENT Reinforced Concrete Slabs 2.0 ANALYSIS AND DESIGN 2.2 STRUCTURAL ELEMENT Reinforced Concrete Slabs Rearrangement by :- NOR AZAH BINTI AIZIZ KOLEJ MATRIKULASI TEKNIKAL KEDAH

INTRODUCTION Concrete slabs are similar to beams in the way they span horizontally between supports and may be simply supported, continuously supported or cantilevered. Unlike beams, slabs are relatively thin structural members which are normally used as floors and occasionally as roof systems in multi-storey buildings.

INTRODUCTION Slabs are constructed of reinforced concrete poured into formwork. The formwork defines the shape of the final slab when the concrete is cured (set). Concrete slabs are usually 150 to 300 mm deep. It is usually timber but steel is commonly used on commercial projects. on-site or into trenches excavated into the ground.

INTRODUCTION Slabs transmit the applied floor or roof loads to their supports. Slabs may be classified into two main groups depending on whether they are supported on the ground or suspended in a building. It is usually timber but steel is commonly used on commercial projects. on-site or into trenches excavated into the ground.

GROUND SLABS Ground slabs are those slabs that are poured directly into excavated trenches in the ground. They rely entirely on the existing ground for support. The ground must be strong enough to support the concrete slab. Normally, a minimum bearing capacity for slab sites is 50 kPa. The ground (more correctly known in the industry as the foundation)

GROUND SLABS Diagram of slabs with arrow representing applied floor and roof load pointed down to the slab. The slab is supported by foundation and the slabs transmit its load to foundation. In most cases, the foundation easily meets this minimum bearing requirement. However, where clays and silts are present in the soil, the slab may experience stresses. These soils tend to be on reactive sites which are those areas where the volume of soil changes because of its moisture content. This results in the foundation expanding or contracting depending on how much moisture the soil contains. Foundation movements can be significant enough to damage a slab and any other components it supports, such as the brickwork shown in the photo.

SUSPENDED SLABS Suspended slabs are slabs that are not in direct contact with the ground. They form roofs or floors above ground level.

SUSPENDED SLABS The way a slab spans its supports Suspended slabs are grouped into two types: One way slabs - which are supported on two sides two way slabs - which are supported on all four sides. The way a slab spans its supports has a direct impact on the way in which the slab will bend.

ONE-WAY SLAB One way slabs are usually rectangular where the length is two or more times the width. These slabs are considered to be supported along the two long sides only even if there is a small amount of support on the narrow ends.

ONE-WAY SLAB A diagram of a concrete slab with two supporting sides is shown. The width of the slab is also the short span. Rule of Thumb: For ly/lx > 2, design as one-way slab ly = the length of the longer side lx =the length of the shorter side

ONE-WAY SLAB

ONE BEND SLAB It is assumed that; one way slabs bend only in the direction of the short span, so; the main steel reinforcement runs in this direction across the slab.

ONE BEND SLAB A diagram of a concrete slab with two supporting sides is shown. Compression on the slab pushes towards the middle of the slab which causes the slab to bend inwards. Tension is distributed across the supporting sides.

TWO WAY SLAB Two way slabs are approximately square where the length is less than double the width and the slab is supported equally on all four sides. Rule of Thumb: For ly/lx ≤ 2, design as two-way slab ly = the length of the longer side lx =the length of the shorter side

TWO WAY SLAB A diagram of a concrete slab with four supporting sides is shown. The pressure spans equally across the width and length of the concrete slab. Spans equally both direction

TWO WAY SLAB

TWO BEND SLAB These slabs are assumed to bend in both directions, so main steel reinforcement of equal size and spacing is run in both directions.

TWO BEND SLAB A diagram of the compression that occurs in a two bend slab is shown. The pressure runs to the middle of the slab which causes all four sides to bend equally. Compression

Example: Figure shows three floor layouts of a monolithic beam and slab construction. a) State whether the floor panels are one-way or two-way spanning. b) Sketch the tributary areas for all the beams B A1 A 1 2 C 3050mm 7650mm 7050mm

Answer : Panel A-A1/1-2 ly/lx=7050/3050 = 2.3 > 2 one-way slab C 3050mm 7650mm 7050mm Panel A-A1/1-2 ly/lx=7050/3050 = 2.3 > 2 one-way slab Panel B-C/1-2 ly/lx=7650/7050 = 1.1 < 2 two-way slab

EXAMPLE : The beams supporting the floor panel A-A1/1-2 are 350 mm deep and 150 mm thick, and the floor slab is 150 mm thick, given the density of concrete as 24 kN/m3. Calculate the self-weight of the beam A/1-2, considering only the rib of the beam in kN/m Calculate the self-weight of the slab in kN/m2 Calculate ultimate load on beam A/1-2 in kN/m Calculate reaction force at column A/1 B A1 A 1 2 C 3050mm 7650mm 7050mm

ANSWER : a) Self-weight of the rib in kN/m 350 rib 150 7050 A/2 a) Self-weight of the rib in kN/m = 0.150 x (0.350-0.150) x 24 = 0.72kN/m b) Self-weight of the slab in kN/m2 = 0.15 x 24 = 3.6kN/m2 c) rib self-weight = 0.72kN/m slab self-weight = 0.5 x w x lx = 0.5 x 3.6 x 3.05 = 5.49kN/m Ultimate load on beam A/1-2 in kN/m = rib self-weight + slab self- weight = 1.4 x 0.72 + 1.4 x 5.49 = 1.008 + 7.686 = 8.694 kN/m d. Reaction force at column A/1 =8.694 x 7.05/2 =30.64kN

One-way slab Design Design a one way slab supported on two brick wall spanning 3 m c-c. The characteristic dead load ( excluded self weight slab) and characteristic live load supports by the slab are 0.35 kN/m2 and 2.5 kN/m2. ( fcu=25 N/mm2 , fy=250 N/mm2, concrete cover=20 mm and assume bar size=10 mm)

One-way slab Design Fst Fcc (d-0.9x/2) a F cc  x Equation As (d-0.9x/2) a F cc  x 0.9x Concrete compression Steel tension Equation Fcc = 0.45fcuA Fst = 0.95As Where: f cu - Characteristic of concrete strength (30N/mm2) f y - Characteristic of reinforcement strength (460N/mm2) A – area of beam cross section AS – area of reinforcement cross section M – Moment ∑Ma = 0 Fcc (d-0.9x/2) – M = 0 Fcc = Fst

Section A-A h=125 3000 Characteristic Dead load,gk = slab self weight + weigh of services, finishing & ceiling = 24kN/m3x h + 0.35 kN/m2 = 24 x0.125 + 0.35 = kN/m2 Live load, qk = 2.5kN/m2

Factored load on the slab = 1.4 x + 1.6 x = kN/m Gk= 5 x 3000 = kN/m 3000 Qk= 2.5 x 3000 = kN/m Factored load on the slab = 1.4 x + 1.6 x = kN/m

TABLE: Ultimate bending moment and shear force coefficients in one-way spanning

Refer Table: Ultimate bending moment and shear force coefficients in one-way spanning As a continues beam, it is not easy to find shear force and bending moment, so we use diagram given. Use middle interior span & interior support F= 83.88kN/m x 3.05m = 255.83 kN Use M = 0.063 FL =0.063x 256x 3.05 =49kNm

H=125 7625 Fst Fcc d= 125-25-10/2=95mm ∑Ma = 0 Fcc=Fst Fcc (d-0.9x/2) – M = 0 0.45fcu xAx(d-0.9x/2)-49x106=0 0.45x30x0.9xx7.625x(95-0.9x/2) – 49x106 =0 92644x (95-0.45x) - 49x106 = 0 8801180x-416906x2 - 49x106 = 0 416906x2 - 8801180x+ 49x106 = 0 X = -b + b2-4ac X = 5.7mm 2a

Fcc =Fst Fcc = 0.45x30x0.9(5.7)x7.625 =528069N 528069 =0.95xfyxAs Where fy=250 (mild steel) As =52809/237.5 =2223mm2 Lets say for 35 rods; 2223/35 = 64mm2 (1 rod) So size rebar A = Πj2= ΠD2/4=64mm2 D = 64x4/ Π D = 9mm for 1 bar 10mm Spacing = 7625-25(2)/34 = 223mm So use 35R10 - 223 , (35 mild steel bar 10mm dia. with 223 spacing)