4/13/2018 Working Stress Analysis for Concrete Beams | Reinforced Concrete Design Review Start Download View PDF Home Forums Blogs Algebra Trigonometry Geometry Calculus Mechanics Economy CE Math Home » Reinforced Concrete Design » Working Stress Design of Reinforced Concrete Working Stress Analysis for Concrete Beams Consider a relatively long simply supported beam shown below. Assume the load wo to be increasing progressively until the beam fails. The beam will go into the following three stages: 1. Uncrack Concrete Stage – at this stage, the gross section of the concrete will resist the bending which means that the beam will behave like a solid beam made entirely of concrete. 2. Crack Concrete Stage – Elastic Stress range 3. Ultimate Stress Stage – Beam Failure Concrete Beam Crack Stages At section 1: Uncrack stage 1. Actual moment, M < Cracking moment, Mcr 2. No cracking occur 3. The gross section resists bending 4. The tensile stress of concrete is below rupture At Section 2: Boundary between crack and uncrack stages https://www.mathalino.com/reviewer/reinforced-concrete-design/working-stress-analysis-concrete-beams 1/7 4/13/2018 Working Stress Analysis for Concrete Beams | Reinforced Concrete Design Review 1. Actual moment, M = Cracking moment, Mcr 2. Crack begins to form 3. The gross section resists bending 4. The tensile stress of concrete reached the rupture point At Section 3: Crack concrete stage 1. Actual moment, M > Cracking moment, Mcr 2. Elastic stress stage 3. Cracks developed at the tension fiber of the beam and spreads quickly to the neutral axis 4. The tensile stress of concrete is higher than the rupture strength 5. Ultimate stress stage can occur at failure Working Stress Analysis – Uncracked Stage The beam will behave elastically and remains uncracked. The tensile stress of concrete is below rupture. Cracking Moment NSCP 2010, Section 409.6.2.3 Modulus of rupture of concrete, f Cracking moment, M cr r − − ′ = 0.7√ f c MPa f r Ig = yt https://www.mathalino.com/reviewer/reinforced-concrete-design/working-stress-analysis-concrete-beams 2/7 4/13/2018 Working Stress Analysis for Concrete Beams | Reinforced Concrete Design Review Where I = Moment of inertia of the gross section neglecting reinforcement g yt = distance from centroid of gross section to extreme tension fiber Working Stress Analysis – Cracked Stage General Requirement Actual Stresses ≤ Allowable Stresses Internal Couple Method Static equilibrium of internal forces Factor k: fc k = fc + fs n Factor j: j = 1 1 3 k Moment resistance coefficient: R = 1 2 f c kj Moment capacity: Use the smallest of the two Mc = C jd = 1 2 f c kj bd 2 = Rbd 2 https://www.mathalino.com/reviewer/reinforced-concrete-design/working-stress-analysis-concrete-beams 3/7 4/13/2018 Working Stress Analysis for Concrete Beams | Reinforced Concrete Design Review Ms = T jd = As f s jd Transformed Section Method Convert steel area to equivalent concrete area by multiplying As with modular ratio, n. Location of the neutral axis from extreme compression fiber Singly reinforced: 1 2 Doubly reinforced: 2 bx 1 2 = nAs (d − x) 2 bx ′ ′ + (2n − 1)As (x − d ) = nAs (d − x) Cracked section moment of inertia (INA = Icr) 3 Singly reinforced: I bx NA = + nAs (d − x) 3 2 3 Doubly reinforced: I NA = bx 3 ′ ′ + (2n − 1)As (x − d ) 2 + nAs (d − x) 2 Actual stresses (calculate using Flexure Formula) Concrete Mx fc = IN A https://www.mathalino.com/reviewer/reinforced-concrete-design/working-stress-analysis-concrete-beams 4/7 4/13/2018 Working Stress Analysis for Concrete Beams | Reinforced Concrete Design Review Tension steel fs M (d − x) = n IN A Compression steel for doubly reinforced ′ ′ fs M (x − d ) = 2n IN A Tags: Cracking Moment Cracked Stage of Concrete Uncracked Stage of Concrete Internal Couple Method Transformed Section Method Example 01: Total Compression Force at the Section of Concrete Beam Example 02: Moment Capacity of a Concrete Beam Example 03: Compressive Force at the Section of Concrete T-Beam Example 04: Stress of Tension Steel, Stress of Compression Steel, and Stress of Concrete in Doubly Reinforced Beam ‹ Working Stress Design of Reinforced Concrete up Example 01: Total Compression Force at the Section of Concrete Beam › Log in or register to post comments Subscribe to MATHalino.com on YouTube 792 Mabuhay! Please join our community. Login or Register or Login With Facebook SPONSORED LINKS https://www.mathalino.com/reviewer/reinforced-concrete-design/working-stress-analysis-concrete-beams 5/7 4/13/2018 Working Stress Analysis for Concrete Beams | Reinforced Concrete Design Review Custom Search Search We're now on YouTube! Please subscribe. MATHalino YouTube 792 Reinforced Concrete Design Working Stress Design of Reinforced Concrete Working Stress Analysis for Concrete Beams Example 01: Total Compression Force at the Section of Concrete Beam Example 02: Moment Capacity of a Concrete Beam Example 03: Compressive Force at the Section of Concrete T-Beam Example 04: Stress of Tension Steel, Stress of Compression Steel, and Stress of Concrete in Doubly Reinforced Beam Design of Steel Reinforcement of Concrete Beams by WSD Method MATHalino Like Page 38K likes Home • Forums • Blogs • Glossary • Recent About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal MATHalino.com - Pinoy Math Community • Copyright 2017 © Romel Verterra • All rights reserved https://www.mathalino.com/reviewer/reinforced-concrete-design/working-stress-analysis-concrete-beams 6/7 4/13/2018 Working Stress Analysis for Concrete Beams | Reinforced Concrete Design Review https://www.mathalino.com/reviewer/reinforced-concrete-design/working-stress-analysis-concrete-beams 7/7
