Lec 8-9-flexural analysis and design of beamns
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This document discusses the ultimate strength design method for concrete beams. It explains that this method divides the factor of safety such that a larger portion is applied to loads and a smaller portion is applied to material strength. It also describes how to determine the neutral axis location, calculate nominal moment capacity, and minimum beam depth for deflection control. Key aspects covered include Whitney stress blocks, yield strength of steel grades, and equations for moment capacity based on steel yield or concrete crushing.
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Lec 9-flexural analysis and design of beamns
Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
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Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
Lec 10-flexural analysis and design of beamns
Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
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The document discusses ACI reinforcement limits for flexural members, including:
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- Beams must be designed as either tension-controlled or in the transition between tension and compression-controlled to ensure sufficient under-reinforcement.
- Strength reduction factors vary between 0.81-0.90 for beams depending on reinforcement strain, with more brittle compression-controlled sections having lower factors of 0.70.
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1. This document discusses trial sizing, design, and analysis of short columns under concentric axial loads.
2. The criteria for determining if a column is considered short is based on the slenderness ratio being less than a specified value depending on the column cross section shape.
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Lec 9-flexural analysis and design of beamns
Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
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Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
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Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
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Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
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Me211 2
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1. The document contains two engineering problems involving the calculation of stresses in mechanical parts.
2. The first problem calculates the increase in a circular tube's torque capacity if its semicircular cross section is inverted. The capacity increases by a factor of 1.66.
3. The second problem determines the stress in a simply supported floorboard experiencing bending from a moment applied 3 degrees off the z-axis. It finds the stress is 925 psi, higher than the 800 psi if applied along z, and calculates the neutral axis angle as -25.3 degrees.
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This document discusses the design of rectangular beams. It describes singly reinforced beams which have steel reinforcement only in the tensile zone below the neutral axis. It also describes doubly reinforced beams which have steel reinforcement in both the tensile and compressive zones. The key steps in the design of rectangular beams using the working stress method are described, including determining the stress distribution, calculating moments, and sizing the reinforcement. Design considerations like clear cover and bar spacing are also outlined.
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Sheryar Bismil
Student of Mirpur University of Science & Technology(MUST).
Student of Final Year Civil Engineering Department Main campus Mirpur.
Here we Gonna to learn about the basic to depth wise study of Plan Reinforced Concrete-i.
From basis terminology to wide information about the analysis and design of Concrete member like column,Beam,Slab,etc.
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- Strain is a measure of deformation in a material under stress. Normal strain measures changes in length while shear strain measures changes in shape.
- The allowable stress for a material is less than its failure stress to ensure safety under loads. Factor of safety is defined as the ratio of failure stress to allowable stress.
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this slide will clear all the topics and problem related to singly reinforced beam by limit state method, things are explained with diagrams , easy to understand .
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The document contains multiple questions about determining internal forces like normal force, shear force, bending moment, stresses, and strains in structural members. Specifically, it asks the reader to:
1) Determine the internal normal force, shear force, and bending moment at point C in a beam supporting various loads.
2) Find the resultant normal and shear forces in different sections of a member subjected to a 500 lb load.
3) Calculate the normal force, shear force, and bending moment acting on a tray arm supporting loads at point C.
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This document summarizes key concepts in stresses and strains from strength of materials including:
1) Definitions of stress as force per unit area and strain as deformation per original length. Common types of stress include axial/tensile, compressive, shear, and bearing stresses.
2) The proportional relationship between stress and strain for a material below its proportional limit, defined by modulus of elasticity E. Stress and strain can then be calculated from each other.
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1. The document contains two engineering problems involving the calculation of stresses in mechanical parts.
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3. The second problem determines the stress in a simply supported floorboard experiencing bending from a moment applied 3 degrees off the z-axis. It finds the stress is 925 psi, higher than the 800 psi if applied along z, and calculates the neutral axis angle as -25.3 degrees.
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(a) Given: Shear strength = 40 ksi
Diameter of hole = 2.5 in
Compressive stress limit in punch = 50 ksi
Use the punching shear formula to find the maximum thickness:
τ = P/A = 50 ksi
A = πDh/4
Solve for h:
h = 4P/(πDτ) = 4(50 ksi)/(π(2.5 in)(40 ksi)) = 0.625 in
(b) Given: Thickness = 0.25 in
Shear strength = 40 ksi
Compressive stress limit = 50 ksi
Use the
Flow Chart - One Way Joist Construction
This document provides design guidelines for one-way joist slabs. It discusses calculating loads and moments for the top slab and joists. For the top slab, the document describes checking if the un-cracked moment capacity is greater than the factored moment, and if not, calculating temperature and shrinkage reinforcement. For the joists, it outlines calculating span length, thickness, loads, moments and shear, then determining reinforcement by checking the depth of the neutral axis and reinforcement ratios and spacing.
Design Procedure of Singly,Doubly & T-Beam(As Per ACI code)
Content:
-USD(Ultimate Strength Design)
-Classification of beam with respect to design system
-Assumptions
-Evolution of design parameters
-Moment Factors Kn,
-Balanced Reinforcement Ratio b
-Calculating Strength Reduction Factor
-Calculating
-Design procedure for Singly Reinforced Beam
-Design procedure for Doubly Reinforced Beam
-Design procedure for T-Beam
-Appendix
Ch 3-a.pdf
1) The document discusses the flexural analysis and design of reinforced concrete beams. It covers typical beam behavior, stress calculations, flexural equations, and examples of determining nominal moment capacity.
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This document discusses different types of stresses including normal stress, shear stress, bearing stress, and stresses in thin-walled pressure vessels. It provides definitions and formulas for calculating normal stress, shear stress, and bearing stress. For thin-walled pressure vessels, it explains that the tangential stress is twice the longitudinal stress and provides the formulas for calculating each. It also includes example problems calculating stresses in cylindrical and spherical pressure vessels.
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- 1. Plain & Reinforced Concrete-1 CE3601 Lecture # 9 28th Feb 2012 Flexural Analysis and Design of Beams (Ultimate Strength Design of Beams)
- 2. Plain & Reinforced Concrete-1 Ultimate Strength Design of Beams (Strength Design of Beams) Strength design method is based on the philosophy of dividing F.O.S. in such a way that Bigger part is applied on loads and smaller part is applied on material strength. fc’ 0.85fc’ Stress Strain Crushing Strength 0.003 favg favg = Area under curve/0.003 If fc’ ≤ 30 MPa favg = 0.72 fc’ β1 = Average Strength/Crushing Strength β1 = 0.72fc’ / 0.85 fc’ = 0.85
- 3. Plain & Reinforced Concrete-1 Ultimate Strength Design of Beams (contd…) Cc T = Asfs la = d – a/2 N.A. εcu= 0.003 Strain Diagram Actual Stress Diagram Internal Force Diagram In ultimate strength design method the section is always taken as cracked. c = Depth of N.A from the extreme compression face at ultimate stage a = Depth of equivalent rectangular stress diagram. εs h c d b 0.85fc fs 0.85fc a Equivalent Stress Diagram/ Whitney’s Stress Diagram a/2 fs
- 4. Plain & Reinforced Concrete-1 Ultimate Strength Design of Beams (contd…) Actual Stress Diagram 0.85fc 0.85fc Equivalent Stress Diagram/ Whitney’s Stress Diagram c Cc Cca • The resultant of concrete compressive force Cc, acts at the centriod of parabolic stress diagram. • Equivalent stress diagram is made in such a way that it has the same area as that of actual stress diagram. Thus the Cc, will remain unchanged. a/2 ab'0.85fcbf cav a'0.85fc'0.72f cc c '0.85f '0.72f a c c cβa 1
- 5. Plain & Reinforced Concrete-1 Ultimate Strength Design of Beams (contd…) Factor β1 β1 = 0.85 for fc’ ≤ 28 MPa Value of β1 decreases by 0.05 for every 7 MPa increase in strength with a minimum of 0.65 0.65'0.00714f1.064β c1 85.0
- 6. Plain & Reinforced Concrete-1 Determination of N.A. Location at Ultimate Condition CASE-I: Tension Steel is Yielding at Ultimate Condition ys εε or ys ff CASE-II: Tension Steel is Not Yielding at Ultimate Condition yf yε sε ysε or ys ff 0.0015 200,000 300 E f ε y y 0.0021 200,000 420 E f ε y y For 300 grade steel For 420 grade steel
- 7. Plain & Reinforced Concrete-1 CASE-I: Tension Steel is Yielding at Ultimate Condition ysss fAfAT ab'0.85fC cc 2 a da l abffA cys '85.0 For longitudinal Equilibrium T = Cc bf fA a c ys '85.0 1β a c and Cc T = Asfs Internal Force Diagram a/2 la
- 8. Plain & Reinforced Concrete-1 CASE-I: Tension Steel is Yielding at Ultimate Condition (contd…) Nominal Moment Capacity, Mn depending on steel = T x la 2 Mn a dfA ys Design Moment Capacity 2 M bnb a dfA ys Nominal Moment Capacity, Mn depending on Concrete = Cc x la 2 a dab0.85fc'Mn 2 a dab0.85fc'M bnb
- 9. Plain & Reinforced Concrete-1 Minimum Depth for Deflection Control I 1 αΔ 3 (Depth) 1 αΔ For UDL 4 ωLαΔ 3 LωLαΔ Deflection Depends upon Span, end conditions, Loads and fy of steel. For high strength steel deflection is more and more depth is required.
- 10. Plain & Reinforced Concrete-1 Minimum Depth for Deflection Control (Contd…) ACI 318, Table 9.5(a) Steel Grade Simply Supported One End Continuous Both End Continuous Cantilever 300 L/20 L/23 L/26 L/10 420 L/16 L/18.5 L/21 L/8 520 L/14 L/16 L/18 L/7
- 11. Concluded