Calculate bending moment, shear force, and reinforcement requirements for concrete beams
Design and analyze reinforced concrete beams with this calculator. Determine bending moments, shear forces, and reinforcement requirements based on loading conditions and beam dimensions.
The bending moment capacity of a reinforced concrete beam depends on:
For a singly reinforced rectangular beam:
\[ M_n = A_s \times f_y \times (d - \frac{a}{2}) \]
Where:
The shear capacity consists of contributions from:
Total shear capacity: \( V_n = V_c + V_s \)
Concrete contribution (simplified):
\[ V_c = 0.17 \times \sqrt{f'_c} \times b \times d \]
Stirrup contribution:
\[ V_s = \frac{A_v \times f_{yt} \times d}{s} \]
Where:
The required area of tension reinforcement can be calculated from:
\[ A_s = \frac{M_u}{\phi \times f_y \times (d - \frac{a}{2})} \]
Where:
Since \( a \) depends on \( A_s \), this is typically solved iteratively or using:
\[ A_s = \frac{0.85 \times f'_c \times b \times d}{f_y} \times \left(1 - \sqrt{1 - \frac{2 \times M_u}{0.85 \times \phi \times f'_c \times b \times d^2}}\right) \]
| Parameter | Recommendation | Reason |
|---|---|---|
| Minimum reinforcement | \( A_{s,min} = \frac{0.25\sqrt{f'_c}}{f_y} \times b \times d \) (not less than \( \frac{1.4b \times d}{f_y} \)) | Prevent sudden failure upon cracking |
| Maximum reinforcement | Typically limited to ensure ductile failure | Ensure tension-controlled behavior |
| Stirrup spacing | Not greater than d/2 or 600 mm | Ensure effective shear resistance |
| Cover | Typically 25-75 mm depending on exposure | Protect reinforcement from corrosion |
This calculator provides estimates based on simplified analysis methods. For actual structural design: