Provide the formulas for calculating the following: • Loads • Shear forces • Bending moments • Stresses • Areas • Volumes • Mass • Sizes of components for civil concrete structure

Certainly! Below are the general formulas used for calculating loads, shear forces, bending moments, stresses, areas, volumes, mass, and sizes of components for a civil concrete structure:

### 1. Loads
- **Dead Load (DL)**: The weight of the structure itself.
  \[
  DL = \text{Volume of the structure} \times \text{Density of the material}
  \]

- **Live Load (LL)**: Variable loads due to occupancy, furniture, etc.
  \[
  LL = \text{Area} \times \text{Load per unit area}
  \]

- **Wind Load (WL)**: A function of surface area, wind speed, and structure height.
  \[
  WL = 0.613 \times q \times A
  \]
  where \( q = \frac{1}{2} \rho v^2 \) (dynamic pressure), \( A \) = area exposed to wind.

### 2. Shear Forces (V)
- For a simply supported beam:
  \[
  V = R - \text{Load}
  \]
  where \( R \) is the reaction force at supports.

### 3. Bending Moments (M)
- For a simply supported beam with a central load:
  \[
  M = \frac{W \times L}{4}
  \]
  where \( W \) is the total load and \( L \) is the length of the beam.

### 4. Stresses
- **Axial Stress (\(\sigma\))**:
  \[
  \sigma = \frac{P}{A}
  \]
  where \( P \) is the axial load and \( A \) is the cross-sectional area.

- **Bending Stress (\(\sigma_b\))**:
  \[
  \sigma_b = \frac{M \cdot c}{I}
  \]
  where \( M \) is the bending moment, \( c \) is the distance from the neutral axis to the outermost fiber, and \( I \) is the moment of inertia.

### 5. Areas
- **Rectangle**:
  \[
  A = b \times h
  \]
  where \( b\) = base, \( h\) = height.

- **Circle**:
  \[
  A = \pi r^2
  \]

### 6. Volumes
- **Prism (Rectangular)**:
  \[
  V = A \times L
  \]
  where \( A\) is the area of the base, and \( L\) is the height/length.

- **Cylinder**:
  \[
  V = \pi r^2 h
  \]

### 7. Mass (m)
- **Mass of an object**:
  \[
  m = \text{Volume} \times \text{Density}
  \]

### 8. Sizes of Components
- **Beam Size (b, h)**:
  For the design of a beam, generally, it can be estimated based on span and load:
  \[
  \text{Effective Depth, } d \approx \frac{L}{10} \text{ to } \frac{L}{12}
  \]
  
- **Column Size**: Columns are usually determined based on load:
  \[
  A = \frac{P}{f_{c}}
  \]
  where \( f_{c} \) is the permissible compressive strength of concrete.

### Notes
- The formulas provided above are simplified and are to be used for preliminary calculations. Proper design typically involves safety factors, material properties, and local building codes.
- When calculating for real-world applications, consider factors like load combinations, serviceability limits, and structural analysis principles. Always refer to relevant standards (e.g., ACI, Eurocode) and consult a structural engineer for final designs.