Beam Analysis: Maximum Bending Moment Calculation
This problem requires calculating the maximum bending moment in a simply supported beam subjected to a uniformly distributed load (UDL).
Problem Setup
- Beam Type: Simply supported
- Span Length, $L$ = 8 m
- Uniformly Distributed Load, $w$ = 20 kN/m
Maximum Bending Moment Formula
For a simply supported beam carrying a UDL over its entire span, the maximum bending moment ($M_{max}$) occurs at the center of the span and is calculated using the formula:
$ M_{max} = \frac{wL^2}{8} $
Calculation Steps
- Substitute values: Plug the given values of $w$ and $L$ into the formula.
$ M_{max} = \frac{(20 \text{ kN/m}) \times (8 \text{ m})^2}{8} $
- Simplify the expression:
$ M_{max} = \frac{20 \times 64}{8} \text{ kNm} $
- Calculate the result:
$ M_{max} = 20 \times 8 \text{ kNm} $
$ M_{max} = 160 \text{ kNm} $
Conclusion
The maximum bending moment in the simply supported beam is 160 kNm.
Important Questions from Design of Structural Elements
A simply supported RCC beam of span 4 m is supporting a brick wall over its entire span. The brick wall is 250 mm thick and 2 m high. The RCC beam has a depth of 600 mm and width of 250 mm. The density of brick masonry and RCC can be assumed as 18 KN/m³ and 25 KN/m³ respectively. Considering the load of the wall and self-weight of the RCC beam, the maximum bending moment in the beam (in KN-m) will be ____________ [rounded off to two decimal places].
A simply supported beam having effective span of 5 meter is carrying a centrally concentrated load of 16 kN. The maximum bending moment in the beam in kN-m is _______________
Area of tensile steel per meter width of a reinforced concrete slab is 335 sq mm. If 8 mm rods are used as reinforcement, then centre to centre spacing of the reinforcement in mm is _______________
- Which of the following is NOT a mechanism of bond resistance in reinforced concrete?
A single span simply supported reinforced concrete beam ($250 \text{ mm}$ wide and $480 \text{ mm}$ effective depth) is subjected to a concentrated load of $120 \text{ kN}$ at its mid-span. Neglecting self-weight of the beam, the nominal shear stress (MPa) at the support section is __________
