--- title: "Effective height, thickness and slenderness ratio" subject: "Design of Timber and Masonry Structures" chapter: 5 key: "semester_5/design_of_timber_and_masonry_structures:effective-height-length-thickness-slenderness" source: https://www.bctengineer.com/q/semester_5/design_of_timber_and_masonry_structures/effective-height-length-thickness-slenderness site: BCT Engineering --- # Effective height, thickness and slenderness ratio Design of Timber and Masonry Structures · Chapter 5: Design of Masonry Walls for Gravity Loads - Asked in: year not given, 6 marks - Video: [5TH SEM CIVIL ENGINEERING SD-II CHAPTER-7 DESIGN OF MASONRY STRUCTURES PART-2](https://www.youtube.com/watch?v=bzUlS73Vw_Q) — Nilachal Polytechnic College Of Engineering - Answer checked by Claude Sonnet 5.5 on 2026-10-14 - Page: https://www.bctengineer.com/q/semester_5/design_of_timber_and_masonry_structures/effective-height-length-thickness-slenderness - Whole chapter: https://www.bctengineer.com/md/semester_5/design_of_timber_and_masonry_structures/chapter-5 ## Question Define effective height, effective length, effective thickness and slenderness ratio of a masonry wall. State the effective height for different end restraint conditions as per IS 1905 and explain why slenderness is important. ## Short answer Effective height is actual height multiplied by an end restraint factor: 0.75 for full fixity both ends, 0.85 for one fixed/one lateral, 1.0 for lateral only both,1.5 for fixed-free,2.0 for lateral-free. Effective length similarly from horizontal supports. Effective thickness accounts for piers or cavities. Slenderness ratio = effective height/thickness (smaller of H_eff/t_eff or L_eff/t_eff). Buckling reduces capacity, so k_s decreases with SR, and code limits SR to 27. ## Answer #### Definitions - **Effective height ($H_{eff}$)**: the height of the wall that is considered to buckle, obtained by multiplying the actual (unsupported) height $H$ by a factor depending on end restraint. - **Effective length ($L_{eff}$)**: the horizontal length considered to buckle between cross walls or other vertical supports, modified for the edge restraint. - **Effective thickness ($t_{eff}$)**: the thickness used in slenderness calculation. For a solid single leaf wall it is the actual thickness $t$; for a wall with piers or cross walls a stiffness factor increases it (1.0 to 2.0); for a cavity wall it is taken as two-thirds of the sum of the leaf thicknesses. - **Slenderness ratio ($SR$)**: $$ SR = \frac{H_{eff}}{t_{eff}} \quad \text{or} \quad \frac{L_{eff}}{t_{eff}}, \text{ whichever is smaller} $$ For a column, $SR$ is the effective height over the least lateral dimension. #### Effective height (IS 1905) | End condition | $H_{eff}$ | |---|---| | Lateral and rotational restraint at both ends (e.g. RC slabs on both sides) | $0.75H$ | | Lateral and rotational restraint at one end, lateral restraint only at the other | $0.85H$ | | Lateral restraint at both ends, no rotational restraint | $1.0H$ | | Lateral and rotational restraint at one end, other end free | $1.5H$ | | Lateral restraint (no rotation) at one end, other end free | $2.0H$ | ```text slab ====== top fixed free top -> 1.5H / 2.0H || | || H | H || | ground ====== base fixed ######### 0.75 H cantilever ``` #### Importance of slenderness - A slender wall fails by buckling at a stress much lower than the crushing strength. The permissible stress is therefore reduced by $k_s$, which decreases as $SR$ rises. - The code limits $SR$ (27 for load-bearing walls), so walls cannot be made taller or thinner than a certain limit. - Slenderness can be reduced by increasing the thickness, adding piers or cross walls, or providing restraint at the top. ## Check yourself The answer's key points as multiple-choice questions, with the correct option and why. 1. How is the slenderness ratio of a wall defined? A. Actual height / actual length B. H_eff/t_eff or L_eff/t_eff, whichever is smaller C. t_eff / H_eff D. H_eff/t_eff or L_eff/t_eff, whichever is larger Answer: B. SR is effective height or effective length over effective thickness, whichever is smaller; for columns it is effective height over the least lateral dimension. (Key point: Slenderness ratio definition) 2. Which effective height applies when there is lateral and rotational restraint at both ends? A. 0.75H B. 1.0H C. 1.5H D. 2.0H Answer: A. Full restraint at both ends (for example RC slabs both sides) gives 0.75H; lateral restraint only at both ends gives 1.0H; free-end cases give 1.5H or 2.0H. (Key point: Effective height factors) 3. What is the effective thickness of a cavity wall? A. Sum of the leaf thicknesses B. Thickness of one leaf C. Two-thirds of the sum of the leaf thicknesses D. Overall thickness including the cavity Answer: C. For a cavity wall, t_eff is two-thirds of the sum of the leaf thicknesses; a solid single leaf uses actual thickness. (Key point: Effective thickness of cavity wall) 4. Why is slenderness important in masonry design? A. Slender walls fail by crushing at higher stress B. It affects only appearance C. A slender wall buckles at a stress below crushing strength, so k_s reduces the stress and the code limits SR to 27 D. It has no effect if the mortar is strong Answer: C. Slender walls buckle at lower stress; permissible stress is reduced by k_s, and SR is limited to 27 for load-bearing walls. (Key point: Importance of slenderness) ## Related in Design of Timber and Masonry Structures - [Permissible compressive stress of masonry as per IS 1905](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Amasonry-permissible-stress-factors-code) — Design of Timber and Masonry Structures, chapter 5 - [Check of a solid brick wall under gravity load](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Asolid-masonry-wall-gravity-check) — Design of Timber and Masonry Structures, chapter 5 - [Wall with openings: pier loads and check](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Amasonry-wall-with-openings-piers) — Design of Timber and Masonry Structures, chapter 5 - [Out-of-plane bending of a masonry wall](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Aout-of-plane-wall-flexure-check) — Design of Timber and Masonry Structures, chapter 6 - [Multi-storey wall: stresses at each level](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Athree-storey-wall-base-stress-check) — Design of Timber and Masonry Structures, chapter 5 - [Safe load on a brick masonry column](https://www.bctengineer.com/question.md?key=semester_5%2Fdesign_of_timber_and_masonry_structures%3Abrick-masonry-column-safe-load) — Design of Timber and Masonry Structures, chapter 5 ## Related in other subjects - [Diameter to thickness ratio for stress limit](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Apipe-diameter-thickness-ratio-hoop-stress) — Hydraulics, chapter 4 - [Short vs long column; limiting slenderness ratio](https://www.bctengineer.com/question.md?key=semester_3%2Fstrength_of_materials%3Ashort-long-column-slenderness) — Strength of Materials, chapter 8 - [Timber columns by slenderness ratio](https://www.bctengineer.com/question.md?key=semester_6%2Fdesign_of_steel_and_timber_structure%3Atimber-column-types-slenderness) — Design of Steel and Timber Structure, chapter 11 - [Water hammer in 1.2 m steel pipe, wall thickness](https://www.bctengineer.com/question.md?key=semester_4%2Fhydraulics%3Awater-hammer-steel-pipe-thickness-1200mm) — Hydraulics, chapter 4