Consider a RCC slab of effective dimensions 5 m × 2 m and a total depth of 130 mm. This slab is to be reinforced with 12 mm diameter bars with a 20 mm clear cover to a reinforcing bar. The minimum feasible distance of centroids of shorter and longer bars from the bottom fibre of the slab will be ______ respectively.
- A20 mm and 32 mm
- B26 mm and 26 mm
- C26 mm and 38 mmCorrect
- D38 mm and 26 mm
Solution
Concept
Effective depth calculation for multi-layer reinforcement in RCC slabs where shorter span bars are placed at the bottom.
Formula
Centroid of bottom (shorter) bars = Clear Cover + (diashorter / 2) Centroid of top (longer) bars = Clear Cover + diashorter + (dialonger / 2)
Step-by-step solution
1. Identify the given parameters: Clear cover = 20 mm, Bar diameter (both shorter and longer) = 12 mm. 2. Shorter bars are placed at the bottom layer: Distance from bottom fibre = Clear Cover + (12 / 2) = 20 + 6 = 26 mm. 3. Longer bars are placed above the shorter bars: Distance from bottom fibre = Clear Cover + diashorter + (12 / 2) = 20 + 12 + 6 = 38 mm. 4. Therefore, the minimum feasible distances are 26 mm and 38 mm respectively.
Explanation
In a two-way reinforced concrete slab, the main reinforcement is placed in two orthogonal layers. The outer layer (usually shorter span bars placed at the bottom for maximum effective depth) has its centroid at clear cover plus half its diameter. The inner layer (longer span bars resting on top of the shorter bars) has its centroid at clear cover plus the diameter of the shorter bar plus half its own diameter.
Why the other options are wrong
A: Incorrectly calculates the second layer. B: Assumes both layers are at the same depth, which is impossible. D: Inverts the positions of shorter and longer bars.
Shortcut
Remember that the bottom-most bars only add half their diameter to the cover, while the second layer adds the full diameter of the first bar plus half its own diameter.
Common mistake
Adding both bar diameters or assuming both layers are at the same depth from the bottom fibre.
Correct answer: C) 26 mm and 38 mm