If ‘H’ is the height of wall between centers of supports, then the effective height of wall where concrete floors have a bearing on wall irrespective of the direction of span will be:
🔬 Understanding Effective Height
The effective height (Hₑꜰ) of a wall is a calculated height used to determine its slenderness ratio. It is not always the same as the actual clear height (H) between floors. The effective height depends on the degree of restraint provided to the wall at its top and bottom supports. More restraint against rotation and lateral movement leads to a smaller effective height, which means the wall is more stable against buckling.
⚖️ Detailed Analysis of IS 1905 Support Conditions
The question describes a specific support condition: a wall supported by concrete floors that have a bearing on it. This scenario is covered in IS 1905: Code of Practice for Structural Use of Unreinforced Masonry.
(a) 0.75 H
Why it's correct: A reinforced concrete (RCC) slab that bears on a masonry wall provides a very high degree of restraint. It prevents both lateral (sideways) movement and rotation at the top of the wall. According to Table 4 of IS 1905, for a wall provided with lateral and rotational restraint at the top and bottom (which is the case for a wall supporting an RCC slab), the effective height is taken as 0.75 times the clear height (H) between the supports.
Analysis of Other Conditions:
The other options correspond to different, less restrained support conditions:
- (b) 0.85 H: This factor is typically used when there is lateral restraint and only partial rotational restraint at the supports.
- (c) 1.0 H: This is used when the supports provide lateral restraint but no rotational restraint (acting like a hinge or pin connection). This is a common assumption for walls supported by timber floors.
- (d) 1.5 H: This factor is used for a cantilever wall that is fixed at the base but is completely free and unsupported at the top.
💡 Study Tips for Effective Height
- More Restraint = Smaller Factor: The better the support, the smaller the effective height factor. A strong, fixed support like an RCC slab provides the most restraint, hence the smallest factor (0.75).
- Remember the Key Values:
- Fixed/Fixed (RCC Slab): 0.75 H
- Hinged/Hinged (Timber Floor): 1.0 H
- Fixed/Free (Cantilever): 1.5 H or 2.0 H (depending on code)
- Concrete is a "Fix": Associate concrete floors with providing a "fixed" support condition, which leads to the 0.75 H factor.