The pattern of steel reinforcement thuscorresponds to the pattern of positive and negative bending moments within the beam: in regionsof positive bending, steel is placed at the bottom of the cross section in regions of negative bending,steel is placed at the top (Figure 5.21). Unlike wood and steel, which can withstand substantial tensionstress, concrete may be safely stressed only in compression. 5 Appendix Chapter 5 - Reinforced concrete: Beams and slabsĬoncrete beams are reinforced with steel rods (reinforcing bars) in order to resist internal tensionforces within the cross section. Introduction to reinforced concrete | Material properties | Sectional properties | Design approaches | Construction systems | Tension elements | Columns | Beams | Connections | Ch. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike License. We recommend using aĪuthors: Gilbert Strang, Edwin “Jed” Herman Use the information below to generate a citation. Then you must include on every digital page view the following attribution: If you are redistributing all or part of this book in a digital format, Then you must include on every physical page the following attribution: If you are redistributing all or part of this book in a print format, Want to cite, share, or modify this book? This book uses theĬreative Commons Attribution-NonCommercial-ShareAlike License However, suppose we attempted to apply the limit comparison test, using the convergent p − series p − series ∑ n = 1 ∞ 1 / n 3 ∑ n = 1 ∞ 1 / n 3 as our comparison series. Since p = 1 / 2 1, p = 2 > 1, the series ∑ n = 1 ∞ 1 / n 2 ∑ n = 1 ∞ 1 / n 2 converges. These series are both p-series with p = 1 / 2 p = 1 / 2 and p = 2, p = 2, respectively. For example, consider the two series ∑ n = 1 ∞ 1 / n ∑ n = 1 ∞ 1 / n and ∑ n = 1 ∞ 1 / n 2. Similarly, if a n / b n → ∞ a n / b n → ∞ and ∑ n = 1 ∞ b n ∑ n = 1 ∞ b n converges, the test also provides no information. Note that if a n / b n → 0 a n / b n → 0 and ∑ n = 1 ∞ b n ∑ n = 1 ∞ b n diverges, the limit comparison test gives no information.
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