--- title: "Define Ld and lap splice, derive Ld" subject: "Design of RCC Structure" chapter: 6 key: "semester_7/design_of_rcc_structure:define-ld-and-lap-splice-derive" source: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/define-ld-and-lap-splice-derive site: BCT Engineering --- # Define Ld and lap splice, derive Ld Design of RCC Structure · Chapter 6: Design for bond and development length - Asked in: 2079 Bhadra, 2+4 marks - Video: [What is development length? | factors affecting development length | what is Ld | civil tutor | #BBS](https://www.youtube.com/watch?v=pPb2DFlW1QI) — Civil Tutor - Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_7/design_of_rcc_structure/define-ld-and-lap-splice-derive - Whole chapter: https://www.bctengineer.com/md/semester_7/design_of_rcc_structure/chapter-6 ## Question Define development length and lap splice. Derive the expression $L_d \le 1.3\frac{M_1}{V_u} + L_0$ at simply supported end, where symbols have their usual meaning. ## Short answer Development length L_d = 0.87 f_y φ/(4 τ_bd). Lap splice: overlapping bars for force transfer, lap length ≥ L_d (≥30φ in flexural tension). At a simple support, moment M = V_u x; full stress at x = M_1/V_u; available length L_0 + M_1/V_u, with 30% increase, yields L_d ≤ 1.3 M_1/V_u + L_0. ## Answer #### Definitions - **Development length ($L_d$):** the length of bar embedded in concrete that is needed to develop the design stress in the bar through bond: $L_d=\dfrac{\phi\,0.87f_y}{4\tau_{bd}}$. - **Lap splice:** a joint between two bars made by overlapping them side by side for a specified length, so that force passes from one bar to the other through the surrounding concrete. The lap length is at least $L_d$ (and not less than $30\phi$ for flexural tension, $2L_d$ for direct tension and $24\phi$ for compression). #### Derivation of $L_d\le 1.3\dfrac{M_1}{V_u}+L_0$ Near a simple support the shear is nearly constant, so $M=V_ux$. Let $M_1$ be the moment of resistance of the section with all bars stressed to $0.87f_y$. The applied moment reaches $M_1$ at $x=M_1/V_u$ from the support centre, so the bars must be fully developed there. The length of bar available for development is the distance to that section plus the anchorage $L_0$ beyond the support centre: $$ L_{avail}=\frac{M_1}{V_u}+L_0 $$ For the bar to be safe against pull-out, $L_d\le L_{avail}$. The compressive reaction at the support confines the bar and increases bond, so the code allows the first term to be increased by 30%: $$ L_d\le\frac{1.3\,M_1}{V_u}+L_0 $$ Here $M_1$ is the moment of resistance of the section assuming all bars are stressed to $0.87f_y$, $V_u$ is the factored shear at the section, and $L_0$ is the sum of the anchorage beyond the centre of the support and the equivalent anchorage value of any hook or mechanical anchorage. (The limit of the greater of $d$ and $12\phi$ applies to $L_0$ at a point of inflection.) ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. What is a lap splice? A. A bar bent back into a hook B. Two bars overlapped side by side so force passes from one to the other through concrete bond C. Two bars welded end to end D. A bar wrapped by a threaded coupler Answer: B. In a lap splice the force transfers through the surrounding concrete over the lap length. (Key point: Lap splice) 2. What is the minimum lap length for bars in flexural tension? A. Not less than 2Ld only B. Not less than Ld/2 C. Not less than 24φ only D. Not less than Ld and 30φ, whichever is greater Answer: D. For flexural tension the lap must be at least Ld and at least 30φ (2Ld for direct tension, 24φ for compression). (Key point: Lap length) 3. At what distance from the support centre is the bar to be fully developed, given M = Vu x near the support? A. x = d B. x = Vu/M1 C. x = M1/Vu D. x = M1 Vu Answer: C. Setting Vu x = M1 gives x = M1/Vu, the section where bars are stressed to 0.87 fy. (Key point: Section of full development) 4. Why is 1.3 applied to M1/Vu? A. Compressive reaction at the support confines the bar and raises bond by about 30% B. Shear is 30% higher at the support C. Concrete is stronger near the support due to curing D. The bar is in compression at the support Answer: A. The confining reaction enhances bond, so the available length term is increased by 30%. (Key point: Enhancement of bond) ## Close variants set in other exams - [Derive development length expression](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aderive-development-length-expression) — Design of RCC Structure, chapter 6, asked 6× ## Related in Design of RCC Structure - [Define development length and lap splice](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adefine-development-length-and-lap-splice) — Design of RCC Structure, chapter 6 - [Design simply supported beam, 6 m span](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Adesign-simply-supported-beam-6-m) — Design of RCC Structure, chapter 4 - [Two-way slab simply supported, 6x4 m](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Atwo-way-slab-simply-supported-6x4) — Design of RCC Structure, chapter 9 - [Derive Ld and explain its use](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aderive-ld-and-explain-its-use) — Design of RCC Structure, chapter 6 - [Flexural bond stress and Ld proof](https://www.bctengineer.com/question.md?key=semester_7%2Fdesign_of_rcc_structure%3Aflexural-bond-stress-and-ld-proof) — Design of RCC Structure, chapter 6 ## Related in other subjects - [Lateral vibration of a simply supported beam](https://www.bctengineer.com/question.md?key=semester_7%2Ftheory_of_mechanism_and_machine_ii%3Abeam-lateral-vibration-simply-supported) — Theory of Mechanism and Machine II, chapter 10 - [Simply supported I-beam: stress at flange-web junction](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Ai-beam-flange-web-junction-stress) — Strength of Materials, chapter 7 - [Castigliano: central deflection of simply supported beam](https://www.bctengineer.com/question.md?key=semester_5%2Ftheory_of_structures_ii%3Acastigliano-central-deflection-ss-beam-udl) — Theory of Structures II, chapter 2 - [Simply supported T-beam: max bending stresses](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3At-beam-6m-100kn-10kn) — Strength of Materials, chapter 7