Thumb rules for Structural Design | RCC Structures Design of RCC Structural Components In this article, we are going to discuss the minimum standards that are to be followed for the design of Structural components of a building such as Columns, beams, slab and foundation. We will also discuss the minimum safe standards for the reinforcing bars that are to be used for the design of the above mentioned Structural Components. Minimum cross-sectional dimension for a Column: is 9”x9”. But to avoid slenderness ratio problems in multistorey buildings, we prefer a rectangular column design of 9″x12″ which is safer. Also check out: Thumb rules for making a Column Layout
Construction on Site | Design of RCC Structures
Minimum RCC beam size: is 9″x9″. But generally, to maintain uniformity and speed of construction, we design all beams of the same size 9″x12″. But 9″x9″ can also be used safely, according to design. Minimum thickness of RCC slab is 4.5″ because a slab may contain electrical pipes embedded into them which could be 0.5″ or even fatter for internal wiring, which effectively reduces slab depths at certain places, causing cracking, weakening and water leakage during rains. So, a minimum thickness of 4.5″ should be maintained. Minimum size of foundation for a single storey of G+1 building, where soil safe bearing capacity is 30 tonnes per square meter, and the oncoming load on the column does not exceed 30 tonnes, a size of 1m x 1m or 3′ x 3′ should be used. Even if the load is less (for example only 20 tonnes) then also the minimum is 3′x3′ and depth of footing should be atleast 4′ below ground level if not more… Reinforcing bar details (minimum) 1. Columns: 4 bars of 12mm steel rods FE 415 2. Beams: 2 bars of 12 mm in the bottom and 2 bars of 10 mm on the top. 3. Slab a) One Way Slab: Main Steel 8 mm bars @ 6″ C/C and Distribution Steel of 6 mm bars @ 6″ C/C b) Two Way Slab: Main Steel 8 mm bars @ 6″ C/C and Distribution Steel of 8 mm bars @ 9″ C/C 4. Foundation: 6″ of PCC layer comes first. Over than, a tapered or rectangular footing of 12″ thickness is minimum. Steel mesh of 8 mm bars @ 6″ C/C should be laid. In a 3′ x 3′ footing, this would consist of 6 bars of 8 mm on both portions of the steel mesh. Those looking for more information on the design of RCC Structures, check out: Step by step procedure to building design A building is composed of various structural components such as Foundations, Plinth beams, Columns, Beams, Slab, Staircase, Doors and Windows.
Building Design Design of Foundation
Design of Foundation – the most commonly used foundation is Column footing. Calculation of loads in Foundation Design Types of Foundations
Design of Beams Beams are mainly classified into two types: 1. Doubly reinforced beam (most commonly used in RCC Construction) 2. Singly reinforced beam Design of Columns Design of RCC columns
Thumb rules for designing a Column Layout Design of Slabs
Various types of RCC Slabs Design of Simply supported Slab Design of Sunken Slab
Design of Staircase Design of Dog legged Staircase Foundation Design Foundation is the base of any structure. Without a firm foundation, the structure cannot stand. That is the reason why we have to be very cautious with the design of foundations because our entire structure rests on the foundation.
Laying of Column Footing Reinforcement The strength of the foundation determines the life of the structure. As we discussed in the earlier article, design of foundation depends on the type of soil, type of structure and its load. On that basis, the foundations are basically divided into Shallow Foundations and Deep Foundations. In this article, we are going discuss the step by step guide to Column Footing Design…. Reinforced Concrete Footings Footing comprises of the lower end of a column, pillar or wall which i enlarged with projecting courses so as to distribute load.
Footings shall be designed to sustain the applied loads, moments and forces and the induced reactions and to ensure that any settlement which may occur shall be as uniform as possible and the safe bearing capacity of soil is not exceeded. In sloped or stepped footings, the effective cross-section in compression shall be limited by the area above the neutral plane, and the angle of slope or depth and location of steps should be such that the design requirements are satisfied at every section. Design Procedure of Column Footings Here is a step-by-step guide to Column Footing Design:
Column Footing Plan and Section Step 1 Area required for footing
Square = B = (w+w1)/P0 Where, Po = safe bearing capacity of soil w1 = self weight of footing w = self weight of footing For Rectangle = b/d = B/D A=bxd Net upward pressure on the footing q/p = W/A Step 2 Bending Moment Critical section for maximum bending moment is taken at the face of the column For a square footing, Mxx = q x B/8 (L – a)2 Mxx = q x L/8 (B – b)2 Myy = q x B/8 (L – a)2 Step 3 To fix the depth of the footing shall be greater of the following: Depth from bending moment consideration d =square root(M/Qb) where, Q = moment of required factor Depth from shear consideration Check for one way shear Check for two way shear or punching shear
Critical shear for one way shear is considered at a distance ‘d’ from face of the column. Shear force, V = qB [ ½(B – b) d] Nominal shear stress, Tv = k . Tc Tc =
0.16square rootfck
Step 4 Check for two way shear Critical section for two way shear is considered at a distance at a distance d/2 from all the faces of the column. SF, V = q [ B2 – (b + d)2] SF, V = q [L x B – (a + d)(b + d)] Nominal shear stress, Tv = V/2((a+d)(b+d)d) ——- {for a rectangle Tv =
V/4((b+d)d)
Tv =
k . Tc
——- {for a square
k = 0.5 + Beta > 1 Tc =
; [Beta = ratio of sides of the column
0.16square rootfck
Area of steel, Ast = M/((sigma)stjd) How to calculate the total load on the footing? | Building Construction This article has been written on the request from my readers. Engineering students generally get confused when it comes to calculating loads for footings. They ask weird and inappropriate questions regarding the load calculations. This is because they haven’t understood what loads are to be calculated when footing/foundation for a building is designed. Calculation of loads is extremely simple. I hope after reading this article, the queries of many of my readers would get a satisfactory answer. Four loads are to be considered in order to measure total load on the footing: 1. Self load of the column x Number of floors 2. Self load of beams x Number of floors 3. Load of walls coming onto the column
4. Total Load on slab (Dead load + Live load) If you get well versed with load calculations, then calculating the size of the footing and following the procedure for foundation design wouldn’t be a problem. Foundations Foundation of a structure is like the roots of a tree without which the tree cannot stand. The construction of any structure, be it a residence or a skyscraper; starts with the laying of foundations. Before designing the foundation, the type of soil is determined. Depending on whether the soil is hard soil or soft soil, a specific type of foundation is adopted.
Shallow Foundations versus Deep Foundations Foundations are made in various materials… They could be reinforced cement concrete foundations or brick foundations or stone rubble masonry foundations etc. The choice of material to be used in the construction of foundations also depends on the weight of the structure on the ground. The bearing capacity of soil plays a major role in deciding the type of foundation. The safe bearing capacity of soil should be 180N/mm2 to 200N/mm2. Foundations are broadly classified into shallow foundations and deep foundations. The depth of the foundation means the difference of level between the ground surface and the base of the
foundation. If the depth of the foundation is greater than its width the foundation is classified as a deep foundation. Shallow foundations are commonly used in smaller structures such as residences and small buildings whose floor height is limited to 10m whereas Deep Foundations are used in Skyscrapers…. Piles are the most commonly used Deep Foundations used in skyscrapers… Types of Shallow foundations Footings Footings are structural members used to support columns and walls and to transmit their load to the underlying soils. Mats or rafts Combined footings, strap and strip footings Column Footing
In this type of foundation the base of the column is sufficiently enlarged to act as the individual support. The widened base not only provides stability but is useful in distributing the load on sufficient area of the soil.
Column footings are usually used in the foundations of residences and buildings where the soil is hard enough has has sufficient bearing capacity.
Pressure distribution Under a Foundation
The law of distribution of pressure under a foundation depends on the homogeneity of the soil and flexibility of the base. If really the soil is homogeneous and the base of the foundation is flexible, the pressure distribution under the foundation will be uniform. On the contrary if the foundation base is absolutely rigid, the pressure distribution will not be uniform but may follow such pattern.
In our designs it is usual to assume a flexible base and hence to regard the pressure distribution to be uniform. This can be achieved by gradually decreasing the thickness of the base towards the edges so that the base is only as much thick as it is regarded to resist the induced moments and shears.
General rules of Foundation Design While designing a foundation the following points must be borne in mind.
When a soil is yielding soil, a certain amount of settlement must be reduced as much as possible by bringing down the pressure intensities.
It is necessary that a foundation shall be designed so that if at all a settlement should occur, it will be uniform. In other words, the settlement of all the footings must be more or less the same.
This is a very important point in reinforced concrete structures due to the rigid connection between the different components of the structure.
In our next article, we will discuss the procedure of designing an isolated foundation and also justify the foundation design rules mentioned above. Step 1: How to calculate the total load on the footing? | Building Construction This article has been written on the request from my readers. Engineering students generally get confused when it comes to calculating loads for footings. They ask weird and inappropriate questions regarding the load calculations. This is because they haven’t understood what loads are to be calculated when footing/foundation for a building is designed. Calculation of loads is extremely simple. I hope after reading this article, the queries of many of my readers would get a satisfactory answer. Four loads are to be considered in order to measure total load on the footing: 1. 2. 3. 4.
Self load of the column x Number of floors Self load of beams x Number of floors Load of walls coming onto the column Total Load on slab (Dead load + Live load)
If you get well versed with load calculations, then calculating the size of the footing and following the procedure for foundation design wouldn’t be a problem. Step 2: oundation Design Foundation is the base of any structure. Without a firm foundation, the structure cannot stand. That is the reason why we have to be very cautious with the design of foundations because our entire structure rests on the foundation.
Laying of Column Footing Reinforcement The strength of the foundation determines the life of the structure. As we discussed in the earlier article, design of foundation depends on the type of soil, type of structure and its load. On that basis, the foundations are basically divided into Shallow Foundations and Deep Foundations. In this article, we are going discuss the step by step guide to Column Footing Design…. Reinforced Concrete Footings Footing comprises of the lower end of a column, pillar or wall which i enlarged with projecting courses so as to distribute load. Footings shall be designed to sustain the applied loads, moments and forces and the induced reactions and to ensure that any settlement which may occur shall be as uniform as possible and the safe bearing capacity of soil is not exceeded. In sloped or stepped footings, the effective cross-section in compression shall be limited by the area above the neutral plane, and the angle of slope or depth and location of steps should be such that the design requirements are satisfied at every section. Design Procedure of Column Footings Here is a step-by-step guide to Column Footing Design:
Column Footing Plan and Section Step 1 Area required for footing Square = B = (w+w1)/P0 Where, Po = safe bearing capacity of soil w1 = self weight of footing w = self weight of footing For Rectangle = b/d = B/D A=bxd
Net upward pressure on the footing q/p = W/A Step 2 Bending Moment Critical section for maximum bending moment is taken at the face of the column For a square footing, Mxx = q x B/8 (L – a)2 Mxx = q x L/8 (B – b)2 Myy = q x B/8 (L – a)2 Step 3 To fix the depth of the footing shall be greater of the following: Depth from bending moment consideration d =square root(M/Qb) where, Q = moment of required factor Depth from shear consideration Check for one way shear Check for two way shear or punching shear Critical shear for one way shear is considered at a distance ‘d’ from face of the column. Shear force, V = qB [ ½(B – b) d] Nominal shear stress, Tv = k . Tc Tc =
0.16square rootfck
Step 4 Check for two way shear
Critical section for two way shear is considered at a distance at a distance d/2 from all the faces of the column. SF, V = q [ B2 – (b + d)2] SF, V = q [L x B – (a + d)(b + d)] Nominal shear stress, Tv = V/2((a+d)(b+d)d) ——- {for a rectangle Tv =
V/4((b+d)d)
Tv =
k . Tc
——- {for a square
k = 0.5 + Beta > 1 Tc =
; [Beta = ratio of sides of the column
0.16square rootfck
Area of steel, Ast = M/((sigma)stjd) RCC Column A column forms a very important component of a structure. Columns support beams which in turn support walls and slabs. It should be realized that the failure of a column results in the collapse of the structure. The design of a column should therefore receive importance. Supporting the slabs is the main function of the columns… Such slabs are called Simply Supported Slabs. Simply supported slabs could be either one way slab or a two-way slab. It depends on the dimensions of the slab.
Reinforced Cement Concrete Column Plan and Section A column is defined as a compression member, the effective length of which exceeds three times the least lateral dimension. Compression members whose lengths do not exceed three times the least lateral dimension, may be made of plain concrete. In this article, we are going to discuss in detail the basis of classification of columns and different types of reinforcement required for a certain type of column. A column may be classified based on different criteria such as: 1. Based on shape
Rectangle Square Circular Polygon
2. Based on slenderness ratio
Short column, ? ? 12 Long column, ? > 12
3. Based on type of loading
Axially loaded column A column subjected to axial load and unaxial bending A column subjected to axial load and biaxial bending
4. Based on pattern of lateral reinforcement
Tied columns Spiral columns
Minimum eccentricity Emin > l/500 + D/30 >20 Where, l = unsupported length of column in ‘mm’ D = lateral dimensions of column Types of Reinforcements for columns and their requirements Longitudinal Reinforcement
Minimum area of cross-section of longitudinal bars must be atleast 0.8% of gross section area of the column.
Maximum area of cross-section of longitudinal bars must not exceed 6% of the gross cross-section area of the column.
The bars should not be less than 12mm in diameter.
Minimum number of longitudinal bars must be four in rectangular column and 6 in circular column.
Spacing of longitudinal bars measures along the periphery of a column should not exceed 300mm.
Transverse reinforcement
It maybe in the form of lateral ties or spirals.
The diameter of the lateral ties should not be less than 1/4th of the diameter of the largest longitudinal bar and in no case less than 6mm.
The pitch of lateral ties should not exceed
Least lateral dimension
16 x diameter of longitudinal bars (small)
300mm
Helical Reinforcement The diameter of helical bars should not be less than 1/4th the diameter of largest longitudinal and not less than 6mm. The pitch should not exceed (if helical reinforcement is allowed);
75mm 1/6th of the core diameter of the column
Pitch should not be less than,
25mm 3 x diameter of helical bar
Pitch should not exceed (if helical reinforcement is not allowed) Least lateral dimension
16 x diameter of longitudinal bar (smaller) 300mm
Three thumb rules to be followed are as follows: 1. Size of the Columns 2. Distance between Columns 3. Alignment of columns Thumb rule no.1 Size of the columns The size of the columns depends on the total load on the columns. Minimum size of the column should not be less than 9”x9”. 9”x9” columns are to be used for a single storey structure with M15 grade of concrete. In case, 9”x9” column size is to be used for 1 and half storey structure, then it is advised to use M20 grade concrete.
A safe and structurally sound column size for a 1 and half storey structure should not be less than 12”x9” using M15 grade concrete. This should be in your most preferred and practical options list. Thumb rule no.2 Distance between the columns Try to maintain equal distance between the centres of two columns. Always plan a column layout on a grid. The distance between two columns of size 9”x9” should not be more than 4m centre to centre of column. If larger barrier free distances are required then going for larger column size is to be used. The size of the columns increase because of two factors: 1. Increase in the distance between two columns (This increases the dimensions of the columns as well the depth of the beam.) 2. Height of the building (Increase in the number of floors is directly proportional to the dimensions of the columns. Thumb rule no.3 Alignment of Columns A rectangular grid is to be made for placing the columns. This helps in avoiding mistakes and placing in columns can be done in the right way. The columns can preferably be arranged in two different fashions: 1. In a straight line with the help of a grid 2. In a circular fashion for circular buildings. Zigzag arrangement of columns is an absolutely wrong way of working out Structural design. It should be remembered that when columns are erected, beams are laid connecting the columns. The Zigzag column placement causes three major issues: 1. Unbalanced load transfer 2. Problems in wall construction 3. Problems in laying beams If these three thumb rules are followed by Civil Engineering and Architecture students, implementation of wrong Structural design can be prevented.
Column Layout for a residence using the Thumb rules| Building Construction In my earlier article, we discussed three important thumb rules that are to be followed while making a column layout for any building. They are as follows: 1. Size of the Columns 2. Distance between the columns 3. Alignment of Columns In this article, we will see an example of a residence of which column layout is done keeping the above three thumb rules in mind. Column Layout for a residence The residential villa comprises of 1 and half floors. Initially, the column size 9″x12″ had been used with the use of M15 grade of concrete. The builder wanted to save on his budget by making the columns smaller in size. That is why, the columns in the Floor plans below are 9″x9″ in size but the Engineer made sure that M20 grade of concrete would be used for Columns.
Column Layout for a Ground Floor
Column Layout for First Floor Thumb rule no1: Size of the Columns The size of the columns are 9″x9″ with the use of M20 grade of concrete. Thumb rule no.2: Distance between the columns:
The distance between the columns does not exceed 4.5m. Thumb rule no.3: Alignment of Columns The Columns have been arranged on a iron grid pattern. So there is absolutely no question of zigzag walls and zigzag beams which reducing complications in the structure.
RCC Beams RCC beams are cast in cement concrete reinforced with steel bars. Beams take up compressive and add rigidity to the structure. Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (i.e., loads due to an earthquake or wind). The loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent structural compression members. In Light frame construction the joists rest on the beam.
Doubly Reinforced Beam In this article, we are going to discuss types of beam construction and RCC design of Doubly reinforced beam… RCC beam construction is of two types:
Singly reinforced beam Doubly reinforced beam
Singly reinforced beam A singly reinforced beam is a beam provided with longitudinal reinforcement in the tension zone only.
Doubly reinforced beam
Beams reinforced with steel in compression and tension zones are called doubly reinforced beams. This type of beam will be found necessary when due to head room consideration or architectural consideration the depth of the beam is restricted.
The beam with its limited depth, if reinforced on the tension side only, may not have enough moment of resistance, to resist the bending moment.
By increasing the quantity of steel in the tension zone, the moment of resistance cannot be increased indefinitely. Usually, the moment of resistance can be increased by not more than 25% over the balanced moment of resistance, by making the beam over-reinforced on the tension side.
Hence, inorder to further increase the moment of resistance of a beam section of unlimited dimensions, a doubly reinforced beam is provided.
Besides, this doubly reinforced beam is also used in the following circumstances:
The external live loads may alternate i.e. may occur on either face of the member.
For example:
A pile may be lifted in such a manner that the tension and compression zones may alternate.
The loading may be eccentric and the eccentricity of the load may change from one side of the axis to another side.
The member may be subjected to a shock or impact or accidental lateral thrust.
Design procedure for doubly reinforced beam Step 1 Determine the limiting moment of resistance for the given c/s(Mulim) using the equation for singly reinforced beam Mulim = 0.87.fy.Ast1.d [1 – 0.42Xumax] Or Balanced section Ast1 = (0.36.fck.b.Xumax)/(0.87fy)
Step 2 If factored moment Mu > Mulim, then doubly reinforced beam is required to be designed for additional moment. Mu – Mulim = fsc.Asc (d – d’)
[fsc value from page no. 70]
Step 3 Additional area of tension steel Ast2 Ast2 =Asc.fsc/0.87fy Step 4 Total tension steel Ast, Ast = Ast1 + Ast2 RCC Beams RCC beams are cast in cement concrete reinforced with steel bars. Beams take up compressive and add rigidity to the structure. Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (i.e., loads due to an earthquake or wind). The loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent structural compression members. In Light frame construction the joists rest on the beam.
Doubly Reinforced Beam In this article, we are going to discuss types of beam construction and RCC design of Doubly reinforced beam… RCC beam construction is of two types:
Singly reinforced beam Doubly reinforced beam
RCC Beams RCC beams are cast in cement concrete reinforced with steel bars. Beams take up compressive and add rigidity to the structure. Beams generally carry vertical gravitational forces but can also be used to carry horizontal loads (i.e., loads due to an earthquake or wind). The loads carried by a beam are transferred to columns, walls, or girders, which then transfer the force to adjacent structural compression members. In Light frame construction the joists rest on the beam.
Doubly Reinforced Beam In this article, we are going to discuss types of beam construction and RCC design of Doubly reinforced beam… RCC beam construction is of two types:
Singly reinforced beam Doubly reinforced beam
Singly reinforced beam A singly reinforced beam is a beam provided with longitudinal reinforcement in the tension zone only. Doubly reinforced beam
Beams reinforced with steel in compression and tension zones are called doubly reinforced beams. This type of beam will be found necessary when due to head room consideration or architectural consideration the depth of the beam is restricted.
The beam with its limited depth, if reinforced on the tension side only, may not have enough moment of resistance, to resist the bending moment.
By increasing the quantity of steel in the tension zone, the moment of resistance cannot be increased indefinitely. Usually, the moment of resistance can be increased by not more than 25% over the balanced moment of resistance, by making the beam over-reinforced on the tension side.
Hence, in order to further increase the moment of resistance of a beam section of unlimited dimensions, a doubly reinforced beam is provided.
Besides, this doubly reinforced beam is also used in the following circumstances:
The external live loads may alternate i.e. may occur on either face of the member.
For example:
A pile may be lifted in such a manner that the tension and compression zones may alternate.
The loading may be eccentric and the eccentricity of the load may change from one side of the axis to another side.
The member may be subjected to a shock or impact or accidental lateral thrust.
Design procedure for doubly reinforced beam Step 1 Determine the limiting moment of resistance for the given c/s(Mulim) using the equation for singly reinforced beam Mulim = 0.87.fy.Ast1.d [1 – 0.42Xumax] Or Balanced section Ast1 = (0.36.fck.b.Xumax)/(0.87fy) Step 2 If factored moment Mu > Mulim, then doubly reinforced beam is required to be designed for additional moment. Mu – Mulim = fsc.Asc (d – d’) Step 3
[fsc value from page no. 70]
Additional area of tension steel Ast2 Ast2 =Asc.fsc/0.87fy Step 4 Total tension steel Ast, Ast = Ast1 + Ast2 Step One: Given that:
Dimensions of section (b and d) Area of tensile steel (Ast) Modular ratio (m)
Stress-strain diagram From the figure above, we can see that the neutral axis is situated at the centre of gravity of a given section. Therefore, the moments of area on either side are equal.
From the figure above, we can see that the neutral axis is situated at the centre of gravity of a given section. Therefore, the moments of area on either side are equal. Therefore, moment of area on compression side = moment of area on tension side Moment of area on compression side = Area of compression side x distance of c.g. of compression area from N.A. = (bx).(x/2) = bx.x/2 Step Two: Moment of area on tension side = equivalent area of concrete x distance of c.g. of tensile steel from N.A. = (m Ast) x (d-x) = mAst(d-x) Step three: Where, mAst = equivalent area of concrete Therefore, bx.x/2 = mAst (d – x) Numerical Problem An RC beam 200mm wide has an effective depth of 350mm. The permissible stresses in concrete and steel are 5N/mm2 and 140 N/mm2 respectively. Find the depth of neutral axis, area of steel and percentage of steel. (modular ratio (m) = 18.66) Step One: Given that: b = breadth of a rectangular beam = 200mm d = effective depth of a beam = 350mm x = depth of neutral axis below the compression edge = ? Ast = cross-sectional area of steel in tension = ? σcbc = permissible compressive stress in concrete in bending = 5N/mm2
σst = permissible stress in steel = 140 N/mm2 m = modular ratio = 18.66 From the concrete stress diagram, the formula is given as, σcbc/(σst/m) = x/(d – x) 5/(140/18.66) = x/(350-x) Therefore, x = 139.97mm
Numerical Problem Find the position of the neutral axis of a reinforced concrete beam 150mm wide and 400mm deep (effective). Area of tensile steel is 804mm2. (modular ratio = m = 18.66) Step One: Given that: b = breadth of a rectangular beam = 150mm d = effective depth of a beam = 400mm Ast = cross-sectional area of steel in tension = 804mm2 x = depth of neutral axis below the compression edge m = modular ratio = 18.66 Taking moments of area of compression and tension sides about neutral axis, bx.x/2 = mAst (d – x) 150×2/2 = 18.66 x 804 (400 – x) 75×2 = 15002.64(400-x) 75 x2 = 6001056 – 15002.64x x2 + 200x – 80014 = 0 After solving the quadratic equation, we will get two values (a negative value and a positive value)
x = 200mm
The distance between the resultant compressive force (C) and tensile force (T) is called the lever arm, and is denoted by z.
Moment of resistance | Singly reinforced Section From the diagram above, it is clear that the intensity of compressive stress varies from maximum at the top to zero at the neutral axis. Therefore, centre of gravity of the compressive force is at a distance x/3 from the top edge of the section. Therefore, z = d-x/3 Moment of resistance is given by, Mr = C x z = bx (σcbc/2)(d-x/3) OR Mr = T x z = Ast σst(d – x/3) For balanced section, the formula is as follows, Mr = bxc σcbc (d – xc/3)
= Ast σst(d – xc/3)
