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Come to take quiz on Design of reinforced concrete structures
ಉಕ್ಕಿನ ವಿನ್ಯಾಸಕ್ಕಾಗಿ ಬೋಲ್ಟ್ ಸಂಪರ್ಕ
ಬೋಲ್ಟ್ ಸಂಪರ್ಕ (Bolt connection)
ರಚನಾತ್ಮಕ ಸದಸ್ಯರನ್ನು ಸೇರಲು ಬೋಲ್ಟ್ ಸಂಪರ್ಕಗಳನ್ನು ಸಾಮಾನ್ಯವಾಗಿ ನಿರ್ಮಾಣ ಮತ್ತು ಎಂಜಿನಿಯರಿಂಗ್‌ನಲ್ಲಿ ಬಳಸಲಾಗುತ್ತದೆ. ಬೋಲ್ಟ್ ಸಂಪರ್ಕಗಳ ಕೆಲವು ಅನುಕೂಲಗಳು ಮತ್ತು ಅನಾನುಕೂಲಗಳು ಇಲ್ಲಿವೆ:
ಪ್ರಯೋಜನಗಳು:
- ಬಹುಮುಖತೆ: ವಿವಿಧ ರೀತಿಯ ವಸ್ತುಗಳು, ಆಕಾರಗಳು ಮತ್ತು ರಚನಾತ್ಮಕ ಸದಸ್ಯರ ಗಾತ್ರಗಳನ್ನು ಸೇರಲು ಬೋಲ್ಟ್ ಸಂಪರ್ಕಗಳನ್ನು ಬಳಸಬಹುದು.
- ಅನುಸ್ಥಾಪನೆಯ ಸುಲಭ: ಬೋಲ್ಟಿಂಗ್ ತುಲನಾತ್ಮಕವಾಗಿ ಸರಳವಾದ ಪ್ರಕ್ರಿಯೆ, ಮತ್ತು ಇದು ವಿಶೇಷ ಉಪಕರಣಗಳು ಅಥವಾ ಸಲಕರಣೆಗಳ ಅಗತ್ಯವಿರುವುದಿಲ್ಲ. ಅಗತ್ಯವಿದ್ದರೆ ಬೋಲ್ಟ್ ಸಂಪರ್ಕಗಳನ್ನು ಸುಲಭವಾಗಿ ಡಿಸ್ಅಸೆಂಬಲ್ ಮಾಡಬಹುದು ಮತ್ತು ಮರುಜೋಡಿಸಬಹುದು.
- ಸಾಮರ್ಥ್ಯ: ಸರಿಯಾಗಿ ಸ್ಥಾಪಿಸಿದಾಗ, ಬೋಲ್ಟ್ ಸಂಪರ್ಕಗಳು ಕತ್ತರಿ, ಒತ್ತಡ ಮತ್ತು ಬಾಗುವ ಶಕ್ತಿಗಳನ್ನು ವಿರೋಧಿಸುವ ಹೆಚ್ಚಿನ ಸಾಮರ್ಥ್ಯದ ಸಂಪರ್ಕಗಳನ್ನು ಒದಗಿಸಬಹುದು.
- ವೆಚ್ಚ-ಪರಿಣಾಮಕಾರಿ: ಬೋಲ್ಟೆಡ್ ಸಂಪರ್ಕಗಳು ವೆಲ್ಡ್ ಸಂಪರ್ಕಗಳಿಗೆ ವೆಚ್ಚ-ಪರಿಣಾಮಕಾರಿ ಪರ್ಯಾಯವಾಗಬಹುದು, ವಿಶೇಷವಾಗಿ ಸಣ್ಣ ಮತ್ತು ಸರಳವಾದ ರಚನೆಗಳಿಗೆ.
- ತಪಾಸಣೆ: ತುಕ್ಕು, ಹಾನಿ ಅಥವಾ ಆಯಾಸದ ಚಿಹ್ನೆಗಳಿಗಾಗಿ ಬೋಲ್ಟ್ ಸಂಪರ್ಕಗಳನ್ನು ದೃಷ್ಟಿಗೋಚರವಾಗಿ ಪರಿಶೀಲಿಸಲು ಸುಲಭವಾಗಿದೆ.
ಅನಾನುಕೂಲಗಳು:
- ಒತ್ತಡದ ಸಾಂದ್ರತೆ: ಬೋಲ್ಟ್ ಸಂಪರ್ಕಗಳು ಬೋಲ್ಟ್ ರಂಧ್ರಗಳ ಸುತ್ತಲೂ ಒತ್ತಡದ ಸಾಂದ್ರತೆಯನ್ನು ರಚಿಸಬಹುದು, ಇದು ಕಾಲಾನಂತರದಲ್ಲಿ ಆಯಾಸ ಮತ್ತು ವೈಫಲ್ಯಕ್ಕೆ ಕಾರಣವಾಗಬಹುದು.
- ಬೋಲ್ಟ್ ಸಡಿಲಗೊಳಿಸುವಿಕೆ: ಬೋಲ್ಟ್‌ಗಳನ್ನು ಸರಿಯಾಗಿ ಬಿಗಿಗೊಳಿಸದಿದ್ದರೆ, ಅವು ಕಾಲಾನಂತರದಲ್ಲಿ ಸಡಿಲಗೊಳ್ಳಬಹುದು ಮತ್ತು ಸಂಪರ್ಕದ ಸಮಗ್ರತೆಯನ್ನು ರಾಜಿ ಮಾಡಬಹುದು.
- ತುಕ್ಕು: ಬೋಲ್ಟ್‌ಗಳು ಮತ್ತು ಬೀಜಗಳು ಕಾಲಾನಂತರದಲ್ಲಿ ತುಕ್ಕುಗೆ ಒಳಗಾಗುತ್ತವೆ, ಇದು ಸಂಪರ್ಕವನ್ನು ದುರ್ಬಲಗೊಳಿಸುತ್ತದೆ ಮತ್ತು ಅದರ ಬಲವನ್ನು ರಾಜಿ ಮಾಡಬಹುದು.
- ಸೌಂದರ್ಯಶಾಸ್ತ್ರ: ಬೋಲ್ಟ್ ಸಂಪರ್ಕಗಳು ಅಸಹ್ಯಕರವಾಗಿರಬಹುದು ಮತ್ತು ನೋಟವು ಮುಖ್ಯವಾದ ರಚನೆಗಳಿಗೆ ಸೂಕ್ತವಾಗಿರುವುದಿಲ್ಲ.
- ನಿರ್ವಹಣೆ: ಬೋಲ್ಟೆಡ್ ಸಂಪರ್ಕಗಳು ಬಿಗಿಯಾಗಿ ಮತ್ತು ತುಕ್ಕು-ಮುಕ್ತವಾಗಿರುತ್ತವೆ ಎಂದು ಖಚಿತಪಡಿಸಿಕೊಳ್ಳಲು ಆವರ್ತಕ ತಪಾಸಣೆ ಮತ್ತು ನಿರ್ವಹಣೆ ಅಗತ್ಯವಿರುತ್ತದೆ.
బోల్ట్ కనెక్షన్
బోల్ట్ కనెక్షన్
బోల్ట్ కనెక్షన్లు సాధారణంగా నిర్మాణ మరియు ఇంజనీరింగ్లో నిర్మాణాత్మక సభ్యులను చేరడానికి ఉపయోగిస్తారు. బోల్ట్ కనెక్షన్ల యొక్క కొన్ని ప్రయోజనాలు మరియు అప్రయోజనాలు ఇక్కడ ఉన్నాయి
ప్రయోజనాలు:
- బహుముఖ ప్రజ్ఞ: వివిధ రకాల పదార్థాలు, ఆకారాలు మరియు నిర్మాణ సభ్యుల పరిమాణాలలో చేరడానికి బోల్ట్ కనెక్షన్లను ఉపయోగించవచ్చు.
- ఇన్స్టాలేషన్ సౌలభ్యం: బోల్టింగ్ అనేది సాపేక్షంగా సరళమైన ప్రక్రియ, దీనికి ప్రత్యేక ఉపకరణాలు లేదా పరికరాలు అవసరం లేదు. అవసరమైతే బోల్ట్ కనెక్షన్లు కూడా సులభంగా విడదీయబడతాయి మరియు తిరిగి అమర్చబడతాయి.
- బలం: సరిగ్గా ఇన్స్టాల్ చేసినప్పుడు, బోల్టెడ్ కనెక్షన్లు కోత, ఉద్రిక్తత మరియు వంపు శక్తులను నిరోధించగల అధిక-శక్తి కనెక్షన్లను అందించగలవు.
- ఖర్చుతో కూడుకున్నది: బోల్టెడ్ కనెక్షన్లు వెల్డెడ్ కనెక్షన్లకు ఖర్చుతో కూడుకున్న ప్రత్యామ్నాయంగా ఉంటాయి, ప్రత్యేకించి చిన్న మరియు సరళమైన నిర్మాణాలకు.
- తనిఖీ: తుప్పు, నష్టం లేదా అలసట సంకేతాల కోసం బోల్ట్ కనెక్షన్లు దృశ్యమానంగా తనిఖీ చేయడం సులభం.
ప్రతికూలతలు:
- ఒత్తిడి ఏకాగ్రత: బోల్ట్ కనెక్షన్లు బోల్ట్ రంధ్రాల చుట్టూ ఒత్తిడి సాంద్రతలను సృష్టించగలవు, ఇది కాలక్రమేణా అలసట మరియు వైఫల్యానికి దారితీస్తుంది.
- బోల్ట్ వదులు: బోల్ట్లు సరిగ్గా బిగించబడకపోతే, అవి కాలక్రమేణా వదులుగా వస్తాయి మరియు కనెక్షన్ యొక్క సమగ్రతను రాజీ చేస్తాయి.
- తుప్పు: బోల్ట్లు మరియు గింజలు కాలక్రమేణా తుప్పుకు గురవుతాయి, ఇది కనెక్షన్ను బలహీనపరుస్తుంది మరియు దాని బలాన్ని రాజీ చేస్తుంది.
- సౌందర్యం: బోల్ట్ కనెక్షన్లు వికారమైనవి మరియు ప్రదర్శన ముఖ్యమైన నిర్మాణాలకు తగినవి కాకపోవచ్చు.
- నిర్వహణ: బోల్ట్ కనెక్షన్లు బిగుతుగా మరియు తుప్పు పట్టకుండా ఉండేలా చూసుకోవడానికి ఆవర్తన తనిఖీ మరియు నిర్వహణ అవసరం.
Bolted connections
Connections in steel design.
Types of connections:
- Riveted connections.
- Bolted connections.
- Welded connections.
Riveted connections :
A riveted connection is a type of mechanical fastener that is used to join two or more components together. It involves inserting a metal pin (known as a rivet) through aligned holes in the components and then deforming the end of the rivet to secure it in place. Riveted connections are commonly used in the construction of bridges, buildings, and other structures, as well as in manufacturing and engineering applications. The strength of a riveted connection depends on the size and type of rivet used, as well as the material properties of the components being joined. Riveted connections are known for their durability and resistance to loosening, making them a popular choice for many applications.
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Bolted connections :
A bolted connection is a type of fastener that is used to join two or more components together. It involves inserting a bolt through aligned holes in the components and securing it in place with a nut or by threading the end of the bolt. Bolted connections are commonly used in the construction of bridges, buildings, and other structures, as well as in manufacturing and engineering applications. The strength of a bolted connection depends on the size and type of bolt used, as well as the material properties of the components being joined. Bolted connections can be designed to be either tension- or shear-loaded, and are often used in applications where disassembly or adjustment is required. Additionally, bolted connections are relatively easy to install and can be designed to be reusable.
There are several types of bolted connections, including:
- Flange connection: A type of bolted connection used to connect two or more components with a flange, typically used in pipe or ductwork systems.
- Tension connection: A type of bolted connection designed to resist forces acting along the axis of the bolt, typically used in the construction of bridges and buildings.
- Shear connection: A type of bolted connection designed to resist forces acting perpendicular to the axis of the bolt, typically used in the construction of bridges and buildings.
- Slip-critical connection: A type of bolted connection designed to resist shear forces, where the bolts are tightened to a specific torque to prevent slipping between the connected components.
- Friction-grip connection: A type of bolted connection designed to resist shear forces, where the tightness of the bolts provides friction between the connected components to transfer loads.
- Combined tension and shear connection: A type of bolted connection that is designed to resist both tension and shear forces. Each type of bolted connection has specific design considerations, and choosing the right type depends on the load conditions and the requirements of the application.
Types of bolted joints :
- Lap joint: This type of joint is commonly used for joining two parts of the same thickness. The two parts overlap each other and are joined with bolts.
- T-joint: A T-joint is formed when a piece of material is attached to a flat surface at a 90-degree angle. The attachment is made with bolts.
- Butt joint: This type of joint is used to join two parts of equal thickness. The two parts are aligned end-to-end and joined with bolts.
- Corner joint: A corner joint is used to join two parts that meet at a right angle. The two parts are joined with bolts.
- Flange joint: A flange joint is a type of bolted joint that is used to connect two parts that have flanges. The flanges are bolted together to form a tight, leak-proof seal.
- tension joint: A tension joint is a type of bolted joint that is designed to withstand tension forces. The bolts in this type of joint are tightened to a specific torque, which creates tension in the joint and prevents it from coming apart. These are some of the most commonly used bolted joints. The specific type of joint used will depend on the application, load requirements, and design constraints.
Welded connections :
A welded connection is a type of fastener that is used to join two or more metal components together by heating and melting the surfaces to be joined and fusing them into a solid mass. Welding is a commonly used method for fabricating structures and components in the construction, manufacturing, and engineering industries. Welded connections are known for their high strength and ability to resist high loads, making them a popular choice for many applications, such as bridges, buildings, and heavy equipment. The strength of a welded connection depends on several factors, including the type of welding process used, the size and type of filler material used, and the material properties of the components being joined. However, welded connections can be more time-consuming and difficult to install compared to other fastener types
Design of doubly reinforced beam
Text and reference books.
1. Limit State Design of Reinforced Concrete by B. C. Punmia, Ashok Kumar Jain and Arun Kumar Jain, Laxmi, Publications Pvt. Ltd., New Delhi.
2. Fundamentals of reinforced concrete by N. C. Sinha and S. K Roy, S. Chand publishers.
3. Design of Reinforced concrete structures by N.Subramanian, Oxford university press.
4. IS 456- 2000 Code of practice for Reinforced Concrete Structures.
Moment carrying capacity of doubly reinforced beam
Text and reference books.
1. Limit State Design of Reinforced Concrete by B. C. Punmia, Ashok Kumar Jain and Arun Kumar Jain, Laxmi, Publications Pvt. Ltd., New Delhi.
2. Fundamentals of reinforced concrete by N. C. Sinha and S. K Roy, S. Chand publishers.
3. Design of Reinforced concrete structures by N.Subramanian, Oxford university press.
4. IS 456- 2000 Code of practice for Reinforced Concrete Structures.
Design of singly reinforced beam (simply supported beam)
Text and reference books.
1. Hibbeler R. C. (2017). Structural Analysis (9th edition.). Pearson Publishers Pvt Ltd.
2. Ramamrutham S. (2020). Strength of Materials (20thedition.).Dhanpat rai publishing company.
3. Khurmi R. S. (2018). A Textbook Of Strength Of Materials (Revised edition.). S Chand And Company Ltd.
Load carrying capacity of singly reinforced beam
Singly reinforced beams bending moment carrying capacity using indian standard code (IS-456).
Cross sectional dimensions of beam.
Width of beam, W : mm.
Overall depth of beam, D : m.
Effective depth of beam, d : mm.
Effective span of beam, L : m.
Cross sectional dimensions of steel bar.
Total area of steel bar, Ast : mm2.
Material strength properties.
Grade of concrete, fck : N/mm2.
Calculation of neutral axis and type of section. The singly reinforced cross section is checked for under reinforced or over reinforced.
xu/d :
The section is :
The moment of resistance is : N-mm.
or
The moment of resistance is : kN-m.
Calculation of safe load :
Factored load is : kN/m.
Safe working load is : kN/m.
Dead load : kN/m.
Live load : kN/m.
Use this guide book to evaluate under reinforced, balanced, over reinforced section and moment of resistance.
PdfFile
https://www.studyforcivilengineeringtips.com/
Calculate area of steel of singly reinforced beam
Calculate area of steel of singly reinforced beam using (IS 456-2000).
Cross sectional dimensions of beam.
Width of beam, W : mm.
Effective depth of beam, d : mm.
Factored moment.
Moment carrying capacity, Mu : mm2.
Material strength properties.
Grade of concrete, fck : N/mm2.
Calculation of limiting moment of given singly reinforced cross section. This section checks for balanced, under reinforced or over reinforced.
Mulim : kNm
The section is :
Area of steel, A1 : mm2.
or
Area of steel, A2 : mm2.
Use this guide book to evaluate under reinforced, balanced, over reinforced section and moment of resistance.
PdfFile
https://www.studyforcivilengineeringtips.com/
Stress block parameters of singly reinforced beam
Derivation of stress block parameters
- Plane sections to axis remains plane even after bending.
- The maximum strain in concrete at the outermost compression fibre is 0.0035 in bending.
- The tensile strength of concrete is ignored.
- The relationship between the compressive stress distribution and strain in concrete may be assumed to be rectangle, trapezoid, parabola or any shape which result in substantial agreement with the test result.
- For design purposes, compressive strength of concrete = 0.67 x fck.
- Partial safety factor for concrete = 1.5.
- Partial safety factor for steel = 1.15.
- Maximum strain in tension reinforcement in section shall not be less than as shown figure.
- d = Effective depth of beam.
- D = Overall depth of beam.
- b = Width of beam.
- C = Compressive force of concrete.
- T = Tensile force of steel.
- xu = Depth of neutral axis.
- εc = Maximum strain allowed in concrete.
- εy = Maximum strain allowed in steel.
- 0.002 = Strain at maximum characteristic compression strength of concrete is present.
- fck = characteristic compression strength of concrete.
- fck = characteristic yield strength of steel.
Basic Assumptions:
\[{{\rm{\varepsilon }}_{\rm{s}}}{\rm{ = }}\frac{{{f_y}}}{{1.15{E_s}}} + 0.002\]
Stress-strain diagram of singly reinforced rectangular section :
Calculation of stress block parameters:
Depth of parabolic part of stress block ( x1 )
\[\frac{{{x_u}}}{{0.0035}} = \frac{{{x^1}}}{{0.002}}\]
Simplyfy the above equation :
\[{x^1} = \left( {\frac{{0.002}}{{0.0035}}} \right) \times {x_u}\]
Depth of the parabolic curve :
\[{x^1} = \left( {\frac{4}{7}} \right) \times {x_u}\]
Depth of the rectangular portion :
\[{x^{11}} = \left( {\frac{3}{7}} \right) \times {x_u}\]
Area of stress block = Area of rectangular portion + Area under parabolic curve
\[{A_{Total}} = \left( {\frac{3}{7} \times {x_u} \times 0.446 \times {f_{ck}}} \right) + \left( {\frac{2}{3} \times \frac{4}{7} \times {x_u} \times 0.446 \times {f_{ck}}} \right)\]
After simplyfying above equation :
\[{A_{Total}} = 0.36 \times {f_{ck}} \times {x_u}\]
The distance of stress block from the top fiber :
\[{x_c} = \frac{{\left( {\frac{3}{7} \times {x_u} \times 0.446 \times {f_{ck}} \times \left( {\frac{1}{2} \times \frac{3}{7} \times {x_u}} \right)} \right) + \left( {\frac{2}{3} \times \frac{4}{7} \times {x_u} \times 0.446 \times {f_{ck}} \times \left( {\frac{3}{8} \times \frac{4}{7} \times {x_u} + \frac{3}{7} \times {x_u}} \right)} \right)}}{{0.36 \times {f_{ck}} \times {x_u}}}\]
Centroid of stress diagram from top fiber:
\[{x_c} = 0.42 \times {x_u}\]
Calculation of depth of neutral axis:
Depth of neutral axis is obtained by considering equillibrium of internal forces of compression and tension.
Compression force of concrete, C = Average stress x compression area.
\[C = 0.36 \times {f_{ck}} \times b \times {x_u}\]
Tensile force of steel, T = Design yield stress x area of steel.
\[T = 0.87 \times {f_y} \times {A_{st}}\]
Tensile force of steel = Compressive force of concrete.
\[0.36 \times {f_{ck}} \times b \times {x_u} = 0.87 \times {f_y} \times {A_{st}}\]
simplyfying the above equation we get.
\[{x_u} = \left( {\frac{{0.87 \times {f_y} \times {A_{st}}}}{{0.36 \times {f_{ck}} \times b}}} \right)\]
Calculation of lever arm:
Lever arm is the distance between compressive and tensile force.
\[Z = \left( {d - 0.42 \times {x_u}} \right)\]
Calculation of moment of resistance:
Moment of resistance is calculated by using Mu = C x Lever arm.
\[{M_u} = 0.36 \times {f_{ck}} \times b \times {x_u} \times \left( {d - 0.42 \times {x_u}} \right)\]
Moment of resistance is calculated by using Mu = T x Lever arm.
\[{M_u} = 0.87 \times {f_y} \times {A_{st}} \times \left( {d - 0.42 \times {x_u}} \right)\]
Table:
| Grade of steel | Xumax |
|---|---|
| Fe-250 | 0.53d |
| Fe-415 | 0.48d |
| Fe-500 | 0.46d |
Refrence
1. Brooks, J.J & Neville A. M. (2019). Concrete Technology (2nd ed.). Pearson Publishers Pvt Ltd.
2. Shetty, M. S & Jain, A. K. ( 2018). Concrete Technology: Theory And Practice (8thed.).S Chand Publishers Pvt Ltd.
Structural analysis-moment distribution method
Text and reference books.
1. Hibbeler R. C. (2017). Structural Analysis (9th edition.). Pearson Publishers Pvt Ltd.
2. Ramamrutham S. (2020). Strength of Materials (20thedition.).Dhanpat rai publishing company.
3. Khurmi R. S. (2018). A Textbook Of Strength Of Materials (Revised edition.). S Chand And Company Ltd.
Design of Rectangular water tank with L/B greater than or equal to two.
Problem:
Design a rectangular water tank with fixed base for a given capacity in litres.
- Draw cross section of tank showing reinforcement details of vertical wall and base slabs.
- Draw plan of tank showing reinforcement details.
Design steps:
- Capacity of circular water tank ( V ) in liters.
- Length and breadth of tank ( L x B ) in m.
- Free board ( f ) in mm.
- Strength of concrete (ex : M20, M35)
- Strength of steel in (ex : Fe415, Fe-500)
IS: 3370 (Part II) Table 1, Clause 3.3.1 and IS: 456-2000, Clause B-2.1.1 and Table 21.
- Unit weight of water , γ = 9.8 kN/m3.
- Permissible stress in concrete , σcbc.
- Permissible tensile stress in steel , σst.
h = Depth of water tank. This can be found out using following equation.
\[h = \frac{{{W_{capacity}}}}{{L \times B}}\]
Choose required depth of water tank.
Total height tank = depth of the tank + Free board
H = h + f
Check for L/B ratio : If L / B ratio is greater than two. The cantilever action is predominate in wall. Hence, cantilever action is considered for analysis.
Calculate modular ratio.
\[m = \frac{{280}}{{3 \times {\sigma _{cbc}}}}\]
Neutral axis depth factor.
\[n = \frac{{m \times {\sigma _{cbc}}}}{{m \times {\sigma _{cbc}} + \times {\sigma _{st}}}}\]
Lever arm.
\[j = 1 - \frac{n}{3}\]
Moment of resistance.
\[k = \frac{1}{2} \times {\sigma _{cbc}} \times j \times n\]
Design moment at corner.
Provide vertical reinforcement.
\[{M_{long}} = \frac{{\gamma \times {H^3}}}{6}\]
Area of steel due to design bending moment.
\[{A_{st}} = \frac{{{M_{long}}}}{{{\sigma _{st}} \times j \times d}}\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
Provide horizontal reinforcement.
Direct tensile transferred by short wall on long wall.
\[{T_{long}} = \gamma \times \left( {H - h_{c}} \right) \times \frac{B}{2}\]
Area of steel due to direct tension.
\[{A_{st}} = \frac{{{T_{Long}}}}{{{\sigma _{st}}}} \times 1000\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
Provide reinforcement in vertiacal, horizontal direction and in middle span.
Provide reinforcement in horizontal direction.
\[{M_{short}} = \frac{{\gamma \times H \times {h^2}}}{6}\]
Area of steel due to design bending moment.
\[{A_{st}} = \frac{{{M_{short}}}}{{{\sigma _{st}} \times j \times d}}\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
Provide reinforcement in horizontal direction.
Design moment at corner.
Water pressure.
\[{P_h} = \gamma \times \left( {H - {h_c}} \right)\]
Fixed-end moment.
\[{M_{short-end}} = \frac{{{P_h} \times {B^2}}}{{12}}\]
Direct tensile transferred by long wall on short wall.
Area of steel due to design bending moment.
\[{A_{st1}} = \frac{{{M_{short-end}}}}{{{\sigma _{st}} \times j \times d}}\]
Area of steel due to direct tension.
\[{A_{st2}} = \frac{{{T_B}}}{{{\sigma _{st}}}} \times 1000\]
Total area of steel.
\[{A_{st}} = {A_{st1}} + {A_{st2}}\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
Design moment at centre.
\[{M_{middle}} = \gamma \times \left( {H - {h_c}} \right) \times \frac{{{B^2}}}{{24}}\]
\[{A_{st}} = \frac{{{M_{middle}}}}{{{\sigma _{st}} \times j \times d}}\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
The base slab is laid on 75mm thick lean conrete mix. Provide thickness of 150 mm or more to avoid leakage of water.
Provide minimum nominal reinforcement in both direction.
Reinforcement bar should be continuous and bent in junction of rectangular water tank.
Sectional elevation and plan of rectangular water tank.
Indian standard code IS 3370-Part ( 2 ).
Design of Rectangular water tank with L/B ratio less than two.
Problem:
Design a rectangular water tank with fixed base for a given capacity in litres.
- Draw cross section of tank showing reinforcement details of vertical wall and base slabs.
- Draw plan of tank showing reinforcement details.
Design steps:
- Capacity of circular water tank ( V ) in liters.
- Length and breadth of tank ( L x B ) in m.
- Free board ( f ) in mm.
- Strength of concrete (ex : M20, M35)
- Strength of steel in (ex : Fe415, Fe-500)
IS: 3370 (Part II) Table 1, Clause 3.3.1 and IS: 456-2000, Clause B-2.1.1 and Table 21.
- Unit weight of water , γ = 9.8 kN/m3.
- Permissible stress in concrete , σcbc.
- Permissible tensile stress in steel , σst.
h = Depth of water tank. This can be found out using following equation.
\[h = \frac{{{W_{capacity}}}}{{L \times B}}\]
Choose required depth of water tank.
Total height tank = depth of the tank + Free board
H = h + f
Check for L/B ratio : If L / B ratio is the lesser than two. The cantilever action will be from the bottom of the base slab to the one metre above. The rest is affected by horizontal frame action. Hence, it is considered for analysis.
Calculate modular ratio.
\[m = \frac{{280}}{{3 \times {\sigma _{cbc}}}}\]
Neutral axis depth factor.
\[n = \frac{{m \times {\sigma _{cbc}}}}{{m \times {\sigma _{cbc}} + \times {\sigma _{st}}}}\]
Lever arm.
\[j = 1 - \frac{n}{3}\]
Moment of resistance.
\[k = \frac{1}{2} \times {\sigma _{cbc}} \times j \times n\]
The critical section hc is H/4 or 1m. Take higher value.
The water pressure, Ph.
\[{P_h} = \gamma \times \left( {H - {h_c}} \right)\]
Fixed end moment of long wall.
\[{F_l} = \frac{{{P_h} \times {L^2}}}{{12}}\]
Fixed end moment of short wall.
\[{F_s} = \frac{{{P_h} \times {B^2}}}{{12}}\]
Moment distribution taable :
| Members. | Stiffness. | Total joint stiffnes. | Distribution factor. |
|---|---|---|---|
| Short wall | a = 4.E.I / B | a + b | Ds = a / ( a + b ) |
| Short wall | b = 4.E.I / L | Dl = b / ( a + b ) |
Moment distribution taable with formula :
| Short wall. | Ds | Dl | Long wall. |
|---|---|---|---|
| Fs | Fl | ||
| Fs x Ds | Fl x Dl | ||
| Total |
Calculate effective depth.
\[d = \sqrt {\frac{M}{{k \times b}}}\]
Provide sufficient effective depth
\[d = D - {C_{effective}}\]
Direct pull on long wall.
\[{T_L} = {P_h} \times \frac{B}{2}\]
Direct pull on short wall.
\[{T_B} = {P_h} \times \frac{L}{2}\]
Eccentricity of reinforcement from centre of wall.
\[x = \frac{D}{2} - {C_{effective}}\]
Design moment at corner.
\[{M_{end}} = M - {T_L}.x\]
Area of steel due to design bending moment.
\[{A_{st1}} = \frac{{{M_{end}} \times {{10}^6}}}{{{\sigma _{st}} \times j \times d}}\]
Area of steel due to direct tension.
\[{A_{st2}} = \frac{{{T_L}}}{{{\sigma _{st}}}} \times 1000\]
Total area of steel.
\[{A_{st}} = {A_{st1}} + {A_{st2}}\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
Moment at centre.
\[M = \frac{{{P_h} \times {L^2}}}{8} - {M_{corner}}\]
Design moment at centre.
\[{M_{middle}} = M - {T_L}.x\]
Area of steel due to design bending moment.
\[{A_{st1}} = \frac{{{M_{middle}} \times {{10}^6}}}{{{\sigma _{st}} \times j \times d}}\]
Area of steel due to direct tension.
\[{A_{st2}} = \frac{{{T_L}}}{{{\sigma _{st}}}} \times 1000\]
Total area of steel.
\[{A_{st}} = {A_{st1}} + {A_{st2}}\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
Design moment at corner.
\[{M_{end}} = M - {T_B}.x\]
Area of steel due to design bending moment.
\[{A_{st1}} = \frac{{{M_{end}} \times {{10}^6}}}{{{\sigma _{st}} \times j \times d}}\]
Area of steel due to direct tension.
\[{A_{st2}} = \frac{{{T_B}}}{{{\sigma _{st}}}} \times 1000\]
Total area of steel.
\[{A_{st}} = {A_{st1}} + {A_{st2}}\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
Moment at centre.
\[M = \frac{{{P_h} \times {L^2}}}{8} - {M_{corner}}\]
Design moment at centre.
\[{M_{middle}} = M - {T_B}.x\]
Area of steel due to design bending moment.
\[{A_{st1}} = \frac{{{M_{middle}} \times {{10}^6}}}{{{\sigma _{st}} \times j \times d}}\]
Area of steel due to direct tension.
\[{A_{st2}} = \frac{{{T_B}}}{{{\sigma _{st}}}} \times 1000\]
Total area of steel.
\[{A_{st}} = {A_{st1}} + {A_{st2}}\]
Consider the desired bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{Ast}} \times 1000\]
Provide diameter of bar at distance C/C.
Cantilever bending moment.
\[{M_{cantilever}} = \frac{{\gamma \times H \times {h^2}}}{6}\]
Area of steel due to cantilever bending moment.
\[{A_{st}} = \frac{{{M}}}{{{\sigma _{st}} \times j \times d}}\]
Only minimum reinforcement is required.
\[{A_{st}} = 0.3\% \times {t_{wall}} \times 1000\]
Consider the bar diameter.
\[{S_v} = \frac{{As{t_{provided}}}}{{As{t_{required}}}} \times 1000\]
Provide diameter of bar at distance C/C.
The base slab is laid on 75mm thick lean conrete mix. Provide thickness of 150 mm or more to avoid leakage of water.
Provide minimum nominal reinforcement in both direction.
Reinforcement bar should be continuous and bent in junction of rectangular water tank.
Sectional elevation and plan of rectangular water tank.
Indian standard code IS 3370-Part ( 2 ).
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