Roads are made up of several layers that work together to provide a durable pavement surface. The bottom layer is the subgrade, made of compacted soil. Above that is the base layer, made of crushed rock. The top layer is the pavement, which can be asphalt or concrete. These layers distribute vehicle loads across the road structure to provide a smooth and durable driving surface for many years.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This lecture discusses the bearing capacity of foundations. It introduces Terzaghi's bearing capacity theory, which evaluates the ultimate bearing capacity of shallow foundations based on a failure surface geometry. Terzaghi's equation for ultimate bearing capacity is presented. Meyerhof's and Hansen's theories are also introduced, which improved on Terzaghi's theory. Hansen's theory provides a more general bearing capacity equation that can be applied to both shallow and deep foundations. Safety factors are applied to the ultimate bearing capacity to determine allowable bearing capacity for foundation design. Settlement criteria may also control and limit the allowable bearing capacity in some cases.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
- There are four main methods to measure the load carrying capacity of piles: static methods, dynamic formulas, in-situ penetration tests, and pile load tests.
- The ultimate load capacity (Qu) of an individual pile or pile group equals the sum of the point resistance (Qp) at the pile tip and the shaft resistance (Qs) developed along the pile shaft through friction between the soil and pile.
- Meyerhof's method is commonly used to calculate Qp in sand based on the effective vertical pressure at the pile tip multiplied by the bearing capacity factor Nq.
Pavement materials in Road Constructionsrinivas2036
Different pavement materials used in the road construction. Importance of soil, aggregate pavement materials. Tests on Soil for pavement construction. Tests on aggregate for pavement construction.
Requirements of soil and aggregates in pavement.
This document discusses the design of continuous beams. It notes that continuous beams must be designed to resist hogging moments at supports in addition to sagging moments in spans. An example three-span continuous beam is then designed. The beam has a total factored load of 80.57 kN/m and 6.1m spans. Elastic analysis finds maximum moments of 239.94 kN.m in end spans and -299.80 kN.m at interior supports. The beam is designed with a depth of 530mm and reinforcement is checked for bending, shear, development length, and deflection requirements.
Roads are made up of several layers that work together to provide a durable pavement surface. The bottom layer is the subgrade, made of compacted soil. Above that is the base layer, made of crushed rock. The top layer is the pavement, which can be asphalt or concrete. These layers distribute vehicle loads across the road structure to provide a smooth and durable driving surface for many years.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
This lecture discusses the bearing capacity of foundations. It introduces Terzaghi's bearing capacity theory, which evaluates the ultimate bearing capacity of shallow foundations based on a failure surface geometry. Terzaghi's equation for ultimate bearing capacity is presented. Meyerhof's and Hansen's theories are also introduced, which improved on Terzaghi's theory. Hansen's theory provides a more general bearing capacity equation that can be applied to both shallow and deep foundations. Safety factors are applied to the ultimate bearing capacity to determine allowable bearing capacity for foundation design. Settlement criteria may also control and limit the allowable bearing capacity in some cases.
Class notes of Geotechnical Engineering course I used to teach at UET Lahore. Feel free to download the slide show.
Anyone looking to modify these files and use them for their own teaching purposes can contact me directly to get hold of editable version.
- There are four main methods to measure the load carrying capacity of piles: static methods, dynamic formulas, in-situ penetration tests, and pile load tests.
- The ultimate load capacity (Qu) of an individual pile or pile group equals the sum of the point resistance (Qp) at the pile tip and the shaft resistance (Qs) developed along the pile shaft through friction between the soil and pile.
- Meyerhof's method is commonly used to calculate Qp in sand based on the effective vertical pressure at the pile tip multiplied by the bearing capacity factor Nq.
Pavement materials in Road Constructionsrinivas2036
Different pavement materials used in the road construction. Importance of soil, aggregate pavement materials. Tests on Soil for pavement construction. Tests on aggregate for pavement construction.
Requirements of soil and aggregates in pavement.
This document discusses the design of continuous beams. It notes that continuous beams must be designed to resist hogging moments at supports in addition to sagging moments in spans. An example three-span continuous beam is then designed. The beam has a total factored load of 80.57 kN/m and 6.1m spans. Elastic analysis finds maximum moments of 239.94 kN.m in end spans and -299.80 kN.m at interior supports. The beam is designed with a depth of 530mm and reinforcement is checked for bending, shear, development length, and deflection requirements.
Slabs are structural members that support transverse loads and transfer them to supports via bending. They are commonly used as floors and roofs. One-way slabs bend in only one direction across the shorter span like a wide beam, while two-way slabs bend in both directions if the ratio of longer to shorter span is less than or equal to 2. Design of one-way slabs involves calculating bending moment and shear force, selecting reinforcement ratio and bar size, and checking deflection, shear, and development length.
Numerical problem bearing capacity terzaghi , group pile capacity (usefulsear...Make Mannan
A 1m wide strip footing is located 0.8m below ground in a c-φ soil. The soil properties are given. Using Terzaghi's analysis with a factor of safety of 3, the safe bearing capacity is calculated to be 112.1 kN/m^2.
A 2m x 3m rectangular footing at a depth of 1.5m in a different c-φ soil is considered. Using Terzaghi's analysis, the safe bearing capacities are calculated to be 471.7 kN/m^2 based on net ultimate capacity and 453.7 kN/m^2 based on ultimate capacity, both with a factor of safety of 3.
This document discusses lateral earth pressure on retaining walls. It introduces Rankine's and Coulomb's theories for estimating active and passive earth pressures. Rankine proposed that a semi-infinite mass of soil could reach states of plastic equilibrium under horizontal stretching (active state) or compression (passive state). Mohr circles are used to determine the principal stresses and orientation of potential failure planes for each state. The active pressure coefficient KA is related to the friction angle, while the passive pressure coefficient KP is also a function of friction angle.
The document provides information on sheet pile structures and cantilever sheet pile walls. It discusses the different types of sheet piles that can be used, including timber, concrete, and steel. It then describes cantilever sheet pile walls and how to analyze them in both granular and cohesive soils. The analysis involves determining the depth of embedment, bending moment, and section modulus of the sheet piles. Finally, it briefly mentions that anchored sheet piles are held in place using anchors and are either free-earth support or fixed-earth support systems.
ppt on construction and design of flexible pavementSUSMITAMAITY4
1) The document summarizes the design and construction of flexible pavements. It describes the typical layers of a flexible pavement from top to bottom including the surface course, binder course, base course, sub-base course, and subgrade.
2) It also discusses factors involved in the design of flexible pavements like traffic load, subgrade soil properties, climate, and required material properties. Common failure modes of flexible pavements include alligator cracking, rutting, and reflection cracking.
3) Design life, traffic calculations, and common tests for bitumen are also outlined. The advantages of flexible pavements include adaptability and ease of repair while the disadvantages include higher maintenance costs and shorter life under heavy traffic loads
This document discusses the design principles, components, and methods for designing both flexible and rigid pavements according to IRC standards, describing the roles of subgrade soil, pavement layers, traffic characteristics, and materials used for flexible pavements consisting of granular bases and bituminous surfaces, as well as jointed concrete slabs for rigid pavements. It also provides an example of designing a two-lane bypass pavement based on initial traffic volume, design life, growth rate, and subgrade CBR value.
The document discusses indeterminate structures, the stiffness method, and its application to structural analysis. It defines indeterminate structures as those that cannot be analyzed using static equilibrium equations alone, as they consist of more members and restraints. The stiffness method is useful for automatically solving problems related to beams, frames, and trusses. It defines stiffness as the end moment required to produce a unit rotation at one end of a member with the other end fixed. Key steps in a stiffness analysis include determining the degree of kinematic indeterminacy, applying restraints, calculating member forces, and solving the equilibrium equations in matrix form to obtain displacements.
Numerical Simulation of Pile using PLAXISDr. Naveen BP
This document summarizes field tests and numerical simulations conducted by Naveen B.P. on various geotechnical structures. It describes field load tests on single piles under vertical and lateral loads. It also discusses numerical modeling of pile load tests in PLAXIS and compares the results to field data. Additionally, it examines soil nailing analysis, lateral monitoring of secant pile walls, and a comparison of FLAC 3D and PLAXIS 3D for laterally loaded pile analysis. The document provides details of field experience with various pile load tests and numerical modeling techniques for evaluating pile behavior.
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
1) The document presents the results of an unconsolidated undrained (UU) triaxial test conducted by a group of 6 students on remolded soil specimens.
2) The UU test involves applying confining pressure to an unsaturated soil sample and shearing it undrained to determine the shear strength parameters. 3 tests were conducted at different confining pressures.
3) The first two tests yielded undrained shear strengths of 45.9 psi and 42.35 psi, while the third test gave a higher value of 55.39 psi, which may not be valid due to partial saturation of that sample.
Cable Layout, Continuous Beam & Load Balancing MethodMd Tanvir Alam
This document provides information on cable layout and load balancing methods for prestressed concrete beams. It discusses layouts for simple, continuous, and cantilever beams. For simple beams, it describes layouts for pretensioned and post-tensioned beams, including straight, curved, and bent cable configurations. It also compares the load carrying capacities of simple and continuous beams. The document concludes by explaining the load balancing method for design, using examples of how to balance loads in simple, cantilever, and continuous beam configurations.
This document discusses consolidation properties and prefabricated vertical drains. It begins by outlining Terzaghi's theory of one-dimensional consolidation, including the assumptions, equations describing pore water flow and changes in void ratio over time. It then discusses how consolidation affects drained and undrained conditions. Prefabricated vertical drains are introduced as a way to accelerate consolidation settlement by improving drainage, shown in a settlement versus time graph comparing performance with and without PVDs.
This document provides information on concrete mix design, including objectives, basic considerations, and the IS (Indian Standards) method for mix design. The objectives of mix design are to achieve the desired workability, strength, durability, and cost. Basic considerations include cost, specifications, workability, strength, durability, and aggregate grading. The IS method is then described in steps, including selecting target strength, water-cement ratio, air content, water and sand contents, cement content, and aggregate contents. An example application of the IS method is also provided.
The document provides information about shear strength of soil. It defines shear strength and its components of cohesion and internal friction. It discusses Mohr's circle of stress and Mohr-Coulomb theory for shear strength. The types of soil are classified based on drainage conditions during shear testing. Common shear strength tests like direct shear test, triaxial test, unconfined compression test and vane shear test are also explained. Sample calculations for shear strength determination from test results are presented.
Cracks in concrete and its remedial measures kamariya keyur
Cracks in concrete can be caused by various factors like plastic shrinkage, drying shrinkage, thermal variations, chemical reactions, errors in design and construction practices, structural overloads, foundation movement, and vegetation. The document classifies cracks as structural or non-structural and describes different types of cracks that can occur before or after concrete hardening. It provides details on the causes and prevention measures for different types of cracks like plastic shrinkage, drying shrinkage, crazing, thermal cracks, cracks due to chemical reactions, and those arising from poor construction practices. The summary focuses on the key information around classification, types, causes and remedies of cracks in concrete structures.
Deep foundations are used when the bearing stratum is located at a significant depth below the surface. The most common types of deep foundations are pile foundations, cofferdams, and caisson foundations. Pile foundations support structures using vertical piles that transfer loads either through end bearing or skin friction. Piles can be made of timber, concrete, steel, or a composite. Cofferdams are temporary structures used to exclude water from a construction site to allow work below the water level. Common types include earthfill, rockfill, single-walled, and cellular cofferdams. Caissons are watertight structures that become part of the permanent foundation. Types are open caissons, box caissons
This document discusses different types of pavements, including flexible, rigid, and semi-rigid pavements. It describes key design factors for both flexible and rigid pavements such as traffic load, pavement materials, subgrade strength assessed by CBR value, and design life. The document emphasizes the importance of pavement design, noting it accounts for nearly half the road construction cost. Good pavements are important as they can easily bear and transmit loads.
This document provides an example of solving a structural analysis problem using the slope-deflection method. It includes:
1) Introducing the slope-deflection equations for a beam with mid-span loading.
2) Presenting a sample frame structure problem and determining it is indeterminate.
3) Writing the slope-deflection equations and equilibrium equations to solve for member end forces and joint rotations.
4) Calculating support reactions based on the member end forces.
5) Drawing the shear and bending moment diagrams.
This document provides definitions and explanations of key concepts in reinforced concrete design. It defines reinforced concrete as a composite material made of concrete and steel reinforcement. The purpose of reinforcement is to improve the tensile strength of concrete. The Limit State Method of design considers both the strength limit state and serviceability limit state, making it a more realistic and economical approach compared to other methods like Working Stress Method and Ultimate Load Method. Key factors of safety in the Limit State Method include partial factors for concrete γc = 1.5, and for steel γs = 1.15.
- The Caissons is used for the purpose of placing a foundation in correct position under water.
- Three types of Caissons
1) Open Caisson
2) Box Caisson
3) Pneumatic Caisson
This document discusses two-way slabs, which deform in two orthogonal directions and require reinforcement in both directions. It describes different types of two-way slabs and analyzes one-way versus two-way slab action. Methods of analysis including Westergaard's theory and Rankine-Grashoff method are covered. Design procedures are provided for reinforced concrete two-way slabs based on Indian code IS 456, including equations to calculate bending moments and requirements for reinforcement.
This document section discusses two-way slabs, which are slabs that span in two orthogonal directions. It covers the analysis and design of two-way slabs using the equivalent frame method. Key points include:
1) Two-way slabs can be flat plates, flat slabs, or slabs with beams. The equivalent frame method models the slab system as a series of frames.
2) Moments from frame analysis are distributed to column strips and middle strips. Design moments are calculated per unit width.
3) Tendon layouts are similar to continuous beams, with minimum spacing and reinforcement also specified. Analysis considers features like equivalent columns.
Slabs are structural members that support transverse loads and transfer them to supports via bending. They are commonly used as floors and roofs. One-way slabs bend in only one direction across the shorter span like a wide beam, while two-way slabs bend in both directions if the ratio of longer to shorter span is less than or equal to 2. Design of one-way slabs involves calculating bending moment and shear force, selecting reinforcement ratio and bar size, and checking deflection, shear, and development length.
Numerical problem bearing capacity terzaghi , group pile capacity (usefulsear...Make Mannan
A 1m wide strip footing is located 0.8m below ground in a c-φ soil. The soil properties are given. Using Terzaghi's analysis with a factor of safety of 3, the safe bearing capacity is calculated to be 112.1 kN/m^2.
A 2m x 3m rectangular footing at a depth of 1.5m in a different c-φ soil is considered. Using Terzaghi's analysis, the safe bearing capacities are calculated to be 471.7 kN/m^2 based on net ultimate capacity and 453.7 kN/m^2 based on ultimate capacity, both with a factor of safety of 3.
This document discusses lateral earth pressure on retaining walls. It introduces Rankine's and Coulomb's theories for estimating active and passive earth pressures. Rankine proposed that a semi-infinite mass of soil could reach states of plastic equilibrium under horizontal stretching (active state) or compression (passive state). Mohr circles are used to determine the principal stresses and orientation of potential failure planes for each state. The active pressure coefficient KA is related to the friction angle, while the passive pressure coefficient KP is also a function of friction angle.
The document provides information on sheet pile structures and cantilever sheet pile walls. It discusses the different types of sheet piles that can be used, including timber, concrete, and steel. It then describes cantilever sheet pile walls and how to analyze them in both granular and cohesive soils. The analysis involves determining the depth of embedment, bending moment, and section modulus of the sheet piles. Finally, it briefly mentions that anchored sheet piles are held in place using anchors and are either free-earth support or fixed-earth support systems.
ppt on construction and design of flexible pavementSUSMITAMAITY4
1) The document summarizes the design and construction of flexible pavements. It describes the typical layers of a flexible pavement from top to bottom including the surface course, binder course, base course, sub-base course, and subgrade.
2) It also discusses factors involved in the design of flexible pavements like traffic load, subgrade soil properties, climate, and required material properties. Common failure modes of flexible pavements include alligator cracking, rutting, and reflection cracking.
3) Design life, traffic calculations, and common tests for bitumen are also outlined. The advantages of flexible pavements include adaptability and ease of repair while the disadvantages include higher maintenance costs and shorter life under heavy traffic loads
This document discusses the design principles, components, and methods for designing both flexible and rigid pavements according to IRC standards, describing the roles of subgrade soil, pavement layers, traffic characteristics, and materials used for flexible pavements consisting of granular bases and bituminous surfaces, as well as jointed concrete slabs for rigid pavements. It also provides an example of designing a two-lane bypass pavement based on initial traffic volume, design life, growth rate, and subgrade CBR value.
The document discusses indeterminate structures, the stiffness method, and its application to structural analysis. It defines indeterminate structures as those that cannot be analyzed using static equilibrium equations alone, as they consist of more members and restraints. The stiffness method is useful for automatically solving problems related to beams, frames, and trusses. It defines stiffness as the end moment required to produce a unit rotation at one end of a member with the other end fixed. Key steps in a stiffness analysis include determining the degree of kinematic indeterminacy, applying restraints, calculating member forces, and solving the equilibrium equations in matrix form to obtain displacements.
Numerical Simulation of Pile using PLAXISDr. Naveen BP
This document summarizes field tests and numerical simulations conducted by Naveen B.P. on various geotechnical structures. It describes field load tests on single piles under vertical and lateral loads. It also discusses numerical modeling of pile load tests in PLAXIS and compares the results to field data. Additionally, it examines soil nailing analysis, lateral monitoring of secant pile walls, and a comparison of FLAC 3D and PLAXIS 3D for laterally loaded pile analysis. The document provides details of field experience with various pile load tests and numerical modeling techniques for evaluating pile behavior.
This ppt is more useful for Civil Engineering students.
I have prepared this ppt during my college days as a part of semester evaluation . Hope this will help to current civil students for their ppt presentations and in many more activities as a part of their semester assessments.
I have prepared this ppt as per the syllabus concerned in the particular topic of the subject, so one can directly use it just by editing their names.
1) The document presents the results of an unconsolidated undrained (UU) triaxial test conducted by a group of 6 students on remolded soil specimens.
2) The UU test involves applying confining pressure to an unsaturated soil sample and shearing it undrained to determine the shear strength parameters. 3 tests were conducted at different confining pressures.
3) The first two tests yielded undrained shear strengths of 45.9 psi and 42.35 psi, while the third test gave a higher value of 55.39 psi, which may not be valid due to partial saturation of that sample.
Cable Layout, Continuous Beam & Load Balancing MethodMd Tanvir Alam
This document provides information on cable layout and load balancing methods for prestressed concrete beams. It discusses layouts for simple, continuous, and cantilever beams. For simple beams, it describes layouts for pretensioned and post-tensioned beams, including straight, curved, and bent cable configurations. It also compares the load carrying capacities of simple and continuous beams. The document concludes by explaining the load balancing method for design, using examples of how to balance loads in simple, cantilever, and continuous beam configurations.
This document discusses consolidation properties and prefabricated vertical drains. It begins by outlining Terzaghi's theory of one-dimensional consolidation, including the assumptions, equations describing pore water flow and changes in void ratio over time. It then discusses how consolidation affects drained and undrained conditions. Prefabricated vertical drains are introduced as a way to accelerate consolidation settlement by improving drainage, shown in a settlement versus time graph comparing performance with and without PVDs.
This document provides information on concrete mix design, including objectives, basic considerations, and the IS (Indian Standards) method for mix design. The objectives of mix design are to achieve the desired workability, strength, durability, and cost. Basic considerations include cost, specifications, workability, strength, durability, and aggregate grading. The IS method is then described in steps, including selecting target strength, water-cement ratio, air content, water and sand contents, cement content, and aggregate contents. An example application of the IS method is also provided.
The document provides information about shear strength of soil. It defines shear strength and its components of cohesion and internal friction. It discusses Mohr's circle of stress and Mohr-Coulomb theory for shear strength. The types of soil are classified based on drainage conditions during shear testing. Common shear strength tests like direct shear test, triaxial test, unconfined compression test and vane shear test are also explained. Sample calculations for shear strength determination from test results are presented.
Cracks in concrete and its remedial measures kamariya keyur
Cracks in concrete can be caused by various factors like plastic shrinkage, drying shrinkage, thermal variations, chemical reactions, errors in design and construction practices, structural overloads, foundation movement, and vegetation. The document classifies cracks as structural or non-structural and describes different types of cracks that can occur before or after concrete hardening. It provides details on the causes and prevention measures for different types of cracks like plastic shrinkage, drying shrinkage, crazing, thermal cracks, cracks due to chemical reactions, and those arising from poor construction practices. The summary focuses on the key information around classification, types, causes and remedies of cracks in concrete structures.
Deep foundations are used when the bearing stratum is located at a significant depth below the surface. The most common types of deep foundations are pile foundations, cofferdams, and caisson foundations. Pile foundations support structures using vertical piles that transfer loads either through end bearing or skin friction. Piles can be made of timber, concrete, steel, or a composite. Cofferdams are temporary structures used to exclude water from a construction site to allow work below the water level. Common types include earthfill, rockfill, single-walled, and cellular cofferdams. Caissons are watertight structures that become part of the permanent foundation. Types are open caissons, box caissons
This document discusses different types of pavements, including flexible, rigid, and semi-rigid pavements. It describes key design factors for both flexible and rigid pavements such as traffic load, pavement materials, subgrade strength assessed by CBR value, and design life. The document emphasizes the importance of pavement design, noting it accounts for nearly half the road construction cost. Good pavements are important as they can easily bear and transmit loads.
This document provides an example of solving a structural analysis problem using the slope-deflection method. It includes:
1) Introducing the slope-deflection equations for a beam with mid-span loading.
2) Presenting a sample frame structure problem and determining it is indeterminate.
3) Writing the slope-deflection equations and equilibrium equations to solve for member end forces and joint rotations.
4) Calculating support reactions based on the member end forces.
5) Drawing the shear and bending moment diagrams.
This document provides definitions and explanations of key concepts in reinforced concrete design. It defines reinforced concrete as a composite material made of concrete and steel reinforcement. The purpose of reinforcement is to improve the tensile strength of concrete. The Limit State Method of design considers both the strength limit state and serviceability limit state, making it a more realistic and economical approach compared to other methods like Working Stress Method and Ultimate Load Method. Key factors of safety in the Limit State Method include partial factors for concrete γc = 1.5, and for steel γs = 1.15.
- The Caissons is used for the purpose of placing a foundation in correct position under water.
- Three types of Caissons
1) Open Caisson
2) Box Caisson
3) Pneumatic Caisson
This document discusses two-way slabs, which deform in two orthogonal directions and require reinforcement in both directions. It describes different types of two-way slabs and analyzes one-way versus two-way slab action. Methods of analysis including Westergaard's theory and Rankine-Grashoff method are covered. Design procedures are provided for reinforced concrete two-way slabs based on Indian code IS 456, including equations to calculate bending moments and requirements for reinforcement.
This document section discusses two-way slabs, which are slabs that span in two orthogonal directions. It covers the analysis and design of two-way slabs using the equivalent frame method. Key points include:
1) Two-way slabs can be flat plates, flat slabs, or slabs with beams. The equivalent frame method models the slab system as a series of frames.
2) Moments from frame analysis are distributed to column strips and middle strips. Design moments are calculated per unit width.
3) Tendon layouts are similar to continuous beams, with minimum spacing and reinforcement also specified. Analysis considers features like equivalent columns.
This document discusses different types of two-way slabs, including edge-supported slabs, column-supported slabs, flat plates, and waffle slabs. It provides details on when a slab is considered a two-way slab and how it is reinforced in two directions to resist bending moments in both directions. The document also discusses analysis methods for two-way slab design.
This document discusses the design of one-way slabs. It begins by defining one-way slabs as slabs that are supported on two opposite sides and carry loads in the perpendicular direction. The document then provides details on: the analysis of one-way slabs as series of 1-foot wide beam strips; typical reinforcement including main tension bars and shrinkage/temperature bars; minimum thickness requirements in the ACI code; and design procedures including selecting design strips, calculating loads, drawing shear and moment diagrams, and determining reinforcement ratios. Examples are provided for reinforcement spacing, minimum cover, and designing a one-way slab.
This document discusses the design of one-way slabs. It begins by defining one-way slabs as slabs that are supported on two opposite sides and carry loads perpendicularly to the supporting beams. The document then outlines the design process, which involves analyzing representative strips of the slab as simple beams and determining reinforcement ratios. Key steps include checking deflection, calculating factored loads, drawing shear and moment diagrams, and selecting reinforcement sizes that satisfy the required ratios. Examples of one-way slab design and the minimum requirements for thickness, reinforcement ratios, and cover are also provided.
The document discusses flat slab construction and design. It begins by defining a flat slab as a reinforced concrete slab without beams that transfers loads directly to supporting columns. It describes various types of flat slabs including simple flat slabs, those with drop panels or column heads, or both. The document outlines design considerations for flat slabs including analyzing column and middle strips, estimating depth, and calculating moments and shear. It also discusses advantages such as reduced height and construction time. In summary, the document provides information on flat slab types, design methodology, and benefits compared to other construction methods.
This document discusses different types of reinforced concrete slabs, including one-way slabs, two-way slabs, flat slabs, and ribbed slabs. One-way slabs are supported on two sides and bend in one direction, while two-way slabs are supported on all four sides and bend in both directions. Flat slabs do not have beams and loads are transferred directly to columns, providing a plain ceiling. Ribbed slabs contain reinforced concrete ribs spaced no more than 1 meter apart between which the slab spans.
Deep beams are structural elements where a significant portion of the load is carried to the supports by compression forces combining the load and reaction. As a result, the strain distribution is nonlinear and shear deformations are significant compared to pure flexure. Examples include floor slabs under horizontal loads, short span beams carrying heavy loads, and transfer girders. The behavior of deep beams is two-dimensional rather than one-dimensional, and plane sections may not remain plane. Analysis requires a two-dimensional stress approach.
This document discusses different types of slabs used in construction. It defines slabs as structural members that provide flat horizontal surfaces. The main types discussed are one-way slabs, which are supported by beams on two sides, and two-way slabs, which are supported on all four sides. The document provides details on the load transfer and reinforcement of each type of slab, and compares the key differences between one-way and two-way slabs. It also briefly discusses grid slabs and defines mechanisms of load transfer in slabs.
1. The document discusses the design of one-way reinforced concrete slabs according to Indian code IS 456:2000.
2. It defines one-way slabs as edge supported slabs spanning in one direction with a ratio of long to short span greater than or equal to 2.
3. The main considerations for slab design discussed are effective span, deflection control, reinforcement requirements including minimum area, maximum bar diameter and cover, and load calculations.
This document provides information about the structural design and drawing course CE8703 taught at Vivekanandha College of Technology for Women. It outlines the course objectives, units, and topics that will be covered. The course aims to provide students with knowledge of structural engineering design principles and the ability to design liquid retaining structures, bridge components, retaining walls, and industrial structures. Specific topics that will be covered include reinforced concrete cantilever retaining walls, flat slab design, liquid storage tanks, steel framing, and girder and connection design. Design methods, code specifications, and drawings will be learned.
The document discusses buckling of columns under axial compression. It describes:
1) Different buckling theories including elastic buckling, inelastic buckling using tangent modulus theory and reduced modulus theory. Shanley's theory accounts for the effect of transverse displacement.
2) Factors affecting buckling strength including end conditions, initial crookedness, and residual stresses. Effective length accounts for end restraint.
3) Local buckling of thin plate elements can reduce the column's strength before its calculated buckling strength is reached. Flange and web buckling must be prevented.
This document discusses the design of reinforced concrete slabs. It begins by introducing different types of slabs used in construction like solid slabs, flat slabs, ribbed slabs, and waffle slabs. It then covers simplified analysis methods for slabs spanning in one or two directions using load and moment coefficients. The document also addresses shear design in slabs, discussing shear stresses and the need for shear reinforcement. It concludes by discussing punching shear analysis around concentrated loads and the importance of limiting span-depth ratios to control deflections in slabs.
Determination of load transfer in reinforced concrete solid slabs by finite e...IOSR Journals
This document analyzes load transfer in reinforced concrete solid slabs using finite element analysis. It models two types of slabs in SAP2000: 1) slabs with pin supports on all four edges and 2) slabs with pin supports at corners and beams along edges. For type 1, stresses are higher in the short direction but still significant in the long direction, showing load is transferred two-way. For type 2, stresses in the short direction increase with stiffer beams while stresses in the long direction decrease. The analysis concludes all concrete solid slabs behave as two-way slabs, transferring load in both directions regardless of dimensions or support conditions.
The document discusses foundations and their design. It defines foundations as structures that transmit loads from superstructures to underlying soil or rock. Foundations are categorized as either shallow or deep depending on their embedment depth. Key factors in selecting a foundation type include loads, subsurface conditions, performance requirements, and materials. Foundation design involves checking bearing capacity, settlement, and structural integrity. Shallow foundations like spread and combined footings are further described in terms of their geometry, loading conditions, and structural design.
1. The document discusses reinforcement in concrete columns. It lists group members for a project and provides information on different types of columns, their load transfer mechanisms, and failure modes.
2. Key points covered include defining short, long, and intermediate columns based on their slenderness ratio. It also discusses calculating the effective length and radius of gyration of a column.
3. The document provides guidelines for steel reinforcement in columns, including minimum bar diameter and concrete cover, as well as the design procedure and considerations for selecting the reinforcement ratio.
The document applies the variational iteration method (VIM) to solve linear and nonlinear ordinary differential equations (ODEs) with variable coefficients. It emphasizes the power of the method by using it to solve a variety of ODE models of different orders and coefficients. The document also uses VIM to solve four scientific models - the hybrid selection model, Thomas-Fermi equation, Kidder equation for unsteady gas flow through porous media, and the Riccati equation. The VIM provides efficient iterative approximations for both analytic solutions and numeric simulations of real-world applications in science and engineering.
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4 slab
1. DESIGN OF SLABS
Dr. G. P. Chandradhara
Professor of Civil Engineering
S. J. College of Engineering
Mysore
1. GENERAL
A slab is a flat two dimensional planar structural element having thickness small compared to its
other two dimensions. It provides a working flat surface or a covering shelter in buildings. It
primarily transfer the load by bending in one or two directions. Reinforced concrete slabs are
used in floors, roofs and walls of buildings and as the decks of bridges. The floor system of a
structure can take many forms such as in situ solid slab, ribbed slab or pre-cast units. Slabs may
be supported on monolithic concrete beam, steel beams, walls or directly over the columns.
Concrete slab behave primarily as flexural members and the design is similar to that of beams.
2. CLASSIFICATION OF SLABS
Slabs are classified based on many aspects
1) Based of shape: Square, rectangular, circular and polygonal in shape.
2) Based on type of support: Slab supported on walls, Slab supported on beams, Slab
supported on columns (Flat slabs).
3) Based on support or boundary condition: Simply supported, Cantilever slab,
Overhanging slab, Fixed or Continues slab.
4) Based on use: Roof slab, Floor slab, Foundation slab, Water tank slab.
5) Basis of cross section or sectional configuration: Ribbed slab /Grid slab, Solid slab,
Filler slab, Folded plate
6) Basis of spanning directions :
One way slab – Spanning in one direction
Two way slab _ Spanning in two direction
In general, rectangular one way and two way slabs are very common and are discussed in detail.
2. 3. METHODS OF ANALYSIS
The analysis of slabs is extremely complicated because of the influence of number of factors
stated above. Thus the exact (close form) solutions are not easily available. The various methods
are:
a) Classical methods – Levy and Naviers solutions(Plate analysis)
b) Yield line analysis – Used for ultimate /limit analysis
c) Numerical techniques – Finite element and Finite difference method.
d) Semi empirical – Prescribed by codes for practical design which uses coefficients.
4. GENERAL GUIDELINES
a. Effective span of slab :
Effective span of slab shall be lesser of the two
1. l = clear span + d (effective depth )
2. l = Center to center distance between the support
b. Depth of slab:
The depth of slab depends on bending moment and deflection criterion. the trail depth
can be obtained using:
• Effective depth d= Span /((l/d)Basic x modification factor)
• For obtaining modification factor, the percentage of steel for slab can be assumed
from 0.2 to 0.5%
• The effective depth d of two way slabs can also be assumed using cl.24.1,IS 456
provided short span is ≤ 3.5m and loading class is < 3.5KN/m2
Type of support Fe-250 Fe-415
Simply supported l/35 l/28
continuous l/40 l/32
3. OR
The following thumb rules can be used
• One way slab d=(l/22) to (l/28).
• Two way simply supported slab d=(l/20) to (l/30)
• Two way restrained slab d=(l/30) to (l/32)
c. Load on slab:
The load on slab comprises of Dead load, floor finish and live load. The loads are calculated
per unit area (load/m2
).
Dead load = D x 25 kN/m2
( Where D is thickness of slab in m)
Floor finish (Assumed as)= 1 to 2 kN/m2
Live load (Assumed as) = 3 to 5 kN/m2
(depending on the occupancy of the building)
5. DETAILING REQUIREMENTS AS PER IS 456 : 2000
a. Nominal Cover :
For Mild exposure – 20 mm
For Moderate exposure – 30 mm
However, if the diameter of bar do not exceed 12 mm, or cover may be reduced by 5 mm.
Thus for main reinforcement up to 12 mm diameter bar and for mild exposure, the nominal
cover is 15 mm
b. Minimum reinforcement : The reinforcement in either direction in slab shall not be less
than
• 0.15% of the total cross sectional area for Fe-250 steel
• 0.12% of the total cross sectional area for Fe-415 & Fe-500 steel.
c. Spacing of bars : The maximum spacing of bars shall not exceed
• Main Steel – 3d or 300 mm whichever is smaller
4. • Distribution steel –5d or 450 mm whichever is smaller
Where, ‘d’ is the effective depth of slab.
Note: The minimum clear spacing of bars is not kept less than 75 mm (Preferably 100 mm)
though code do not recommend any value.
d. Maximum diameter of bar: The maximum diameter of bar in slab, shall not exceed D/8,
where D is the total thickness of slab.
6. BEHAVIOR OF ONE WAY SLAB
When a slab is supported only on two parallel apposite edges, it spans only in the direction
perpendicular to two supporting edges. Such a slab is called one way slab. Also, if the slab is
supported on all four edges and the ratio of longer span(ly) to shorter span (lx) i.e ly/lx > 2,
practically the slab spans across the shorter span. Such a slabs are also designed as one way
slabs. In this case, the main reinforcement is provided along the spanning direction to resist one
way bending.
Fig.1: Behavior of one way slab
5. 7. BEHAVIOR OF TWO WAY SLABS
A rectangular slab supported on four edge supports, which bends in two orthogonal directions
and deflects in the form of dish or a saucer is called two way slabs. For a two way slab the ratio
of ly/lx shall be ≤ 2.0 .
Fig. 2: Behavior of Two way slab
Since, the slab rest freely on all sides, due to transverse load the corners tend to curl up and lift
up. The slab looses the contact over some region. This is known as lifting of corner. These slabs
are called two way simply supported slabs. If the slabs are cast monolithic with the beams, the
corners of the slab are restrained from lifting. These slabs are called restrained slabs. At corner,
the rotation occurs in both the direction and causes the corners to lift. If the corners of slab are
restrained from lifting, downward reaction results at corner & the end strips gets restrained
against rotation. However, when the ends are restrained and the rotation of central strip still
occurs and causing rotation at corner (slab is acting as unit) the end strip is subjected to torsion.
6. 7.1 Types of Two Way Slab
Two way slabs are classified into two types based on the support conditions:
a) Simply supported slab
b) Restrained slabs
7.1.1 Two way simply supported slabs
The bending moments Mx and My for a rectangular slabs simply supported on all four edges
with corners free to lift or the slabs do not having adequate provisions to prevent lifting of
corners are obtained using
Mx = αx W l2
x
My = αy W l2
x
Where, αx and αy are coefficients given in Table 1 (Table 27,IS 456-2000)
W- Total load /unit area
lx & ly – lengths of shorter and longer span.
Table 1 Bending Moment Coefficients for Slabs Spanning in Two Directions at
Right Angles, Simply Supported on Four Sides (Table 27:IS 456-2000)
ly/lx 1.0 1.1 1.2 1.3 1.4 1.5 1.75 2.0 2.5 3.0
αx 0.062 0.074 0.084 0.093 0.099 0.104 0.113 0.118 0.122 0.124
αy 0.062 0.061 0.059 0.055 0.05 1 0.046 0.037 0.029 0.020 0.014
Note: 50% of the tension steel provided at mid span can be curtailed at 0.1lx or 0.1ly from
support.
7.1.2 Two way Restrained slabs
When the two way slabs are supported on beam or when the corners of the slabs are prevented
from lifting the bending moment coefficients are obtained from Table 2 (Table 26, IS456-2000)
depending on the type of panel shown in Fig. 3. These coefficients are obtained using yield line
7. theory. Since, the slabs are restrained; negative moment arises near the supports. The bending
moments are obtained using;
Mx (Negative)= αx
(-)
W l2
x
Mx (Positive)= αx
(+)
W l2
x
My (Negative)= αy
(-)
W l2
x
My (Positive)= αy
(+)
W l2
x
Fig. 3: Different Boundary conditions of Two way Restrained slabs
8. Table 2: Bending moment coefficients for two way restrained slabs ( Table 26, IS 456-2000)
Detailing requirements as per IS 456-2000
a. Slabs are considered as divided in each direction into middle and end strips as shown
below
b. The maximum moments obtained using equations are apply only to middle strip.
c. 50% of the tension reinforcement provided at midspan in the middle strip shall extend in
the lower part of the slab to within 0.25l of a continuous edge or 0.15l of a discontinuous
edge and the remaining 50% shall extend into support.
d. 50% of tension reinforcement at top of a continuous edge shall be extended for a distance
of 0.15l on each side from the support and atleast 50% shall be provided for a distance of
0.3l on each face from the support.
9. e. At discontinuous edge, negative moment may arise, in general 50% of mid span steel
shall be extended into the span for a distance of 0.1l at top.
f. Minimum steel can be provided in the edge strip
g. Tension steel shall be provided at corner in the form of grid (in two directions) at top and
bottom of slab where the slab is discontinuous at both the edges . This area of steel in
each layer in each direction shall be equal to ¾ the area required (Ast) for maximum mid
span moment. This steel shall extend from the edges for a distance of lx/5. The area of
steel shall be reduced to half (3/8 Astx) at corners containing edges over only one edge is
continuous and other is discontinuous.
Fig. 4: Reinforcement details and strips in Two way restrained slabs
10. 8. ONE WAY CONTINUOUS SLAB
The slabs spanning in one direction and continuous over supports are called one way
continuous slabs.These are idealised as continuous beam of unit width. For slabs of uniform
section which support substantially UDL over three or more spans which do not differ by
more than 15% of the longest, the B.M and S.F are obtained using the coefficients
available in Table 12 and Table 13 of IS 456-2000. For moments at supports where two
unequal spans meet or in case where the slabs are not equally loaded, the average of the two
values for the negative moments at supports may be taken. Alternatively, the moments may
be obtained by moment distribution or any other methods.
Table 3: Bending moment and Shear force coefficients for continuous slabs
( Table 12, Table 13, IS 456-200)
11. DESIGN EXAMPLES
1. Design a simply supported one –way slab over a clear span of 3.5 m. It carries a live load of
4 kN/m2
and floor finish of 1.5 kN/m2
. The width of supporting wall is 230 mm. Adopt M-
20 concrete & Fe-415 steel.
1) Trail depth and effective span
Assume approximate depth d =L/26
3500/26 = 134 mm
Assume overall depth D=160 mm & clear cover 15mm for mild exposure
d = 160-15 (cover) -10/2 (dia of Bar/2) =140 mm
Effective span is lesser of the two
i. l =3.5 + 0.23 (width of support) = 3.73 m
ii. l= 3.5 + 0.14 (effective depth) =3.64 m
effective span = 3.64 m
2) Load on slab
i. Self weight of slab = 0.16 x 25 = 4.00
ii. Floor finish = 1.50
iii. Live load = 4.00
= 9.5 kN/m2
Ultimate load Wu = 9.5 x 1.5 = 14.25 kN/m2
3) Design bending moment and check for depth
Mu = Wul2
/8 = 23.60 kN/m
Minimum depth required from BM consideration
d= = = 92.4 > 140 (OK)
4) Area of Reinforcement
Area of steel is obtained using the following equation
Mu=
12. 23.60X106
=
23.60X106
=50547Ast-749
Solving Ast =504mm2
OR
Ast=
Ast =
=505 mm2
Spacing of 10mm SV=
SV= =154 mm
Provide 10mm @ 150 C/C ( )
(420 or 300 ) OK
Provided steel (Ast=524mm2
,Pt=0.37%)
Distribution steel@ 0.12% of the Gross area.
=192 mm2
Spacing of 8 mm SV= =260 mm
Provide 8 mm @260 mm C/C (<5d or 450)
(700 or 450) OK
5) Check for shear
Design shear Vu=
= = 25.93 kN
13. (< )
Shear resisted by concrete (Table 19, IS 456-2000)
However for solid slab design shear strength shall be
=
Where, K is obtained from Cl.40.2.1.1, IS 456 -2000
OK
6) Check for deflection
k1- Modification factor for tension steel
k2 – Modification factor for compression steel
k3 – Modification factor for T-sections k4-Only
if span exceeds 10 m (10/span)
(Fig. 4,cl.32.2.1)
=20X1.38=27.6
=3630/140=25.92
(OK)
7) Check for Development length
Development length
Ld = (0.87x415x10) / (4x1.2x1.6) =470 mm
14. At simple support, where compressive reaction confines the bars, to limit the dia. of bar
Since alternate bars are cranked M1=Mu/2 = 23.2/2 = 11.8 kN.m
V1 = 5.93 kN., Providing 90o bend and 25 mm end cover
Lo = 230/2 – 25 + 3(dia of bar) = 120
470 < (1.3x11.8x106) / (25.9x103) + 120 = 711 mm O. K.
However, from the end anchorage requirement
extend the bars for a length equal to ld/3 = 156 mm from inner face of support
8) Check for cracking
• Steel is more than 0.12% of the gross area.
• Spacing of steel is < 3d
• Diameter of bar used is < 160/8=20mm
Check for cracking is satisfied.
Reinforcement Detail of One way slab
15. 2. Design a R.C Slab for a room measuring 6.5mX5m. The slab is cast monolithically over the
beams with corners held down. The width of the supporting beam is 230 mm.The slab
carries superimposed load of 4.5kN/m2
. Use M-20 concrete and Fe-500 Steel.
Since, the ratio of length to width of slab is less than 2.0 and slab is resting on beam, the slab is
designed as two way restrained slab (case-9)
1) Trail depth and effective span
Assume approximate depth d=l/30=5000/30=166mm
Assume D=180 mm & clear cover 15 mm for mild exposure
d=180-15-10/2=160 mm.
Effective span is lesser of the two
i). ly=6.5+0.23=6.73 m , lx=5.0+0.23=5.23 m
ii). ly=6.5+0.16=6.66 m, lx=5+0.16=5.16 m
ly= 6.66 m lx= 5.16 m
2) Load on slab
i). Self weight of slab=0.18X25=4.50 kN/m2
ii). Super imposed load =4.50
9.0 kN/m2
Ultimate load wu = 9X1.5=13.5 kN/m2
3) Design bending moment and check for depth
The boundary condition of slab in all four edges discontinuous (case 9, Table 9.5.2)
Mx = αx Wu l2
x
My = αy Wu l2
x
For ly/lx =1.3, αx=0.079
αy=0.056
Positive moment at mid span of short span =Mx= 0.079X13.5X5.162
=28.40 kN.m
16. Positive moment at mid span of longer span =My=0.056X13.5X5.162
=20.13 kN.m
Minimum depth required from Maximum BM consideration
d= = =103 mm
However, provide d=160 mm
4) Area of Reinforcement
Mu=
Steel along shorter direction (Mx)
28.17X106
=
28.40X106
=69600Ast-10.875
Solving x=438 mm2
Provide 10 mm@ 175 C/C (Pt =0.27%)
Steel along longer direction (My)
Since long span bars are placed above short span bars d=160-10=150
20.13X106
=
20.13X106
=65250Ast- 10.875
Solving, =327 mm2
Spacing at 10 mm;
Provide 10 mm @ 240 mm c/c (<3d=450)
5) Check for shear & development
Check for shear and development length are generally satisfied in case of slab and hence they are
not checked.
6) Check for deflection
17. k1 =1.5 for pt=0.27% & fs=0.58xfy = 240
( Fig.4, Cl 32.2.1, IS 456-200)
=26X1.5=39
=5.16/0.16=32
(OK)
7) Check for cracking
Since steel is more than 0.12% of the gross area,
Spacing of steel is <3d and
Diameter of bar used is <D/8=180/8=22 mm OK.
Detailing
Torsion steel
Area of Torsion steel=0.75X Ast =0.75X438=328 mm2
Provide 8 mm bars at spacing (50/328)X1000=152 mm.
Size of mesh =(lx/5)=5160/5=1032 mm
Provide 8 mm @ 150 c/c in both direction for a length of 1035 mm mesh at top and bottom
The calculated steel in shorter and longer direction is to be provided only in the middle strip.
The steel in the edge strip contains only 0.12% of the gross area
Steel in the edge strip=(0.12/100)X1000X180=216 mm2
Spacing of 8 mm (50/216)X1000=230 mm c/c.
19. 3. A hall in a building of clear dimension 14.10 mX9.7 m is to be provided a floor consisting of
a continuous slab cast monolithically with 300 mm wide beams spaced at 3.6 m c/c and
supported on 300 mm wall at ends. The floor is to support a live load of 3 kN/m2
, Partition
load of 1.0 kN/m2
and finishes at 1.0 kN/m2
. Design the continuous slab taking M-20 grade
of concrete and Fe-415 steel.
1) Trail depth and Effective span
Consider 1 m width of slab and effective span shall be taken equal to c/c of beams
Assume trail depth d = l /30 , 3600/30 =120 mm
OR
Assume Pt=0.3%, Modification factor K1 =1.2;
Basic (L/d) ratio for continuous slab =26.
Trail depth d=3600/(26X1.2) = 115 mm.
However, Assume Total depth =150 mm, Dia of bar 10 mm and nominal cover 15 mm
Effective depth d= 150-15-10/2 = 130 mm.
2) Load on slab
a) Total Dead load
i). Self weight of slab= 0.15 x 25 = 3.75 kN/m2
ii). Floor Finish = 1.00
iii). Partition load = 1.00
Total = 5.75 kN/m2
Factored Dead load Wd=1.5 x5.75=8.625 kN/m2
b) Factored live load WL=1.5 x3.00=4.50 kN/m2
3) Design bending moment
The bending moments and shear force are calculated at different sections using Bending
moment coefficient given in Table 12 and Table 13 of IS 456-2000
B.M at any section
20. i). B.M at middle of end span
(1)= kN-m
ii). B.M at middle of Interior span(3)=
iii). B.M at support next to end support(2)=
iv). B.M at other intermediate support(4)=
Depth required from maximum B.M considerations
d= (for Fe 415 steel)
d= = 80 mm > 130 mm OK.
4) Area of Reinforcement
From practical consideration, Spacing cannot be varied at different locations. Hence steel is
calculated only at middle of end span and at support next to end support.
Ast at middle of end span
Mu=
15.15X106
=
15.15X106
=46936Ast, p-7.49
Ast, p =341 mm2
Spacing of 8 mm = 146 mm
Provide 8 mm @ 145 c/c (349 mm2
)
Ast at support next to end support
17.66X106
=
21. Solving, Ast, N =402 mm2
Provide 8 mm @ 280 c/c + 10 mm @ 280 c/c
Area of steel provided= (OK)
(Pt=0.34%)
Distribution steel @ 0.12 % of gross area
Spacing of 8 mm Sv = mm
Provide 8 mm @ 275 c/c ( <5d or 450, OK)
5) Check for deflection
Steel provided at mid span is considered
=340 (Pt =0.26%)
Design stress fs =0.58 x 415X 240 N/mm2
From Figure M.F= 1.52 ( Fig. 4, Cl 32.2.1, IS 456-200)
6) Check for shear
Maximum shear occurs at support next to end support (outer side)
Max. S.F =
=(0.6 x 8.625 +0.6 x 4.5)3.6
= 28.35 kN.
Nominal shear stress
= N/mm2
For M-20 concrete with Pt =0.35 (at support)
22. N/mm2
For solid slab shear strength = k.
k = 1.3 (for thickness 150 mm & less )
=1.3 x 0.4 =0.52 N/mm2
> 0.22 N/mm2
(OK)
7) Check for cracking
Since steel is more than 0.12% of the gross area,
Spacing of steel is <3d and
Diameter of bar used is 8 and 10 mm and are < D/8=150/8=19 mm
(OK)
Reinforcement Detail of One way Continuous slab