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Thinking about the relationship:
- An arch is the key structural element in a (stone/masonry) bridge โ it defines and enables the bridge's spanning ability.
- A dome is the key structural/spatial element that defines a rotunda โ a circular room covered by a dome.
A rotunda is specifically a round building or room topped with a dome. Famous examples: Pantheon (Rome), US Capitol Rotunda.
A pendentive is the transitional element between a square base and a dome โ not the completed building type. A vault is a different structural form. A minaret is a tower.
Plain cement concrete (PCC):
- Very high compressive strength (~20โ50 MPa for standard mixes)
- Very low tensile strength (~1/10th of compressive = 2โ5 MPa)
- This is why steel reinforcement is added (RCC) โ steel handles tension, concrete handles compression.
Structural steel has high strength in both tension and compression. Timber has moderate strength in both. RCC is a composite with improved tensile properties.
Among single materials, PCC best demonstrates this extreme disparity.
Down the group, bond length increases (HโX bond gets weaker), making it easier to release Hโบ. Therefore acid strength increases down the group:
\(\text{H}_2\text{O} < \text{H}_2\text{S} < \text{H}_2\text{Se} < \text{H}_2\text{Te}\)
Note: This trend is opposite to electronegativity trend, and is governed by bond dissociation energy.
Young's Formula for pediatric dosage calculation:
\[\text{Child's dose} = \frac{\text{Age (years)}}{\text{Age (years)} + 12} \times \text{Adult dose}\]
Calculation:
\[\text{Child's dose} = \frac{6}{6 + 12} \times 300\,\text{mg}\]
\[= \frac{6}{18} \times 300\,\text{mg}\]
\[= \frac{1}{3} \times 300\,\text{mg} = 100\,\text{mg}\]
Other pediatric dose formulas:
| Formula | Method |
|---|---|
| Young's | \(\dfrac{\text{Age}}{\text{Age}+12} \times \text{Adult dose}\) (for children) |
| Dilling's | \(\dfrac{\text{Age}}{20} \times \text{Adult dose}\) |
| Clark's (weight) | \(\dfrac{\text{Weight (kg)}}{70} \times \text{Adult dose}\) |
| Fried's (infants) | \(\dfrac{\text{Age (months)}}{150} \times \text{Adult dose}\) |
| BSA method | \(\dfrac{\text{Child's BSA (m}^2\text{)}}{1.73} \times \text{Adult dose}\) โ most accurate |
BSA-based dosing is most precise in clinical practice. Young's formula is used when weight is unavailable.
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