9.Consider the following conditions 1) Concentrated loads are placed near beam supports. 2) The depth of beam section is small, and the beam is loaded uniformly. Question - the design of a beam is governed by shear under which of the following conditions?
Condition 1: Concentrated loads placed near beam supports.** When concentrated loads are applied near supports, the shear force at the support is high due to the short distance from the load to the reaction point. This results in a relatively low bending moment but high shear stress. Consequently, shear is likely to govern the design to prevent shear failure, such as diagonal tension or shear cracking.
- **Condition 2: The depth of the beam section is small, and the beam is loaded uniformly.** A small depth (shallow beam) reduces the cross-sectional area, which lowers the shear capacity. However, under uniform loading, the maximum bending moment (at midspan) is typically more critical for shallow beams. This is because the bending stress is inversely proportional to the square of the depth (\( \sigma \propto 1/d^2 \)), making bending failure more likely than shear failure. Additionally, for uniformly loaded beams, the shear force is usually highest at supports but is often mitigated by support conditions, while bending dominates over most of the span. Therefore, this condition does not typically govern shear design.
Based on this analysis: - Condition 1 alone causes the design to be governed by shear. - Condition 2 does not cause the design to be governed by shear.
When concentrated loads are applied near supports, the shear force at the support is high due to the short distance from the load to the reaction point. This results in a relatively low bending moment but high shear stress. Consequently, shear is likely to govern the design to prevent shear failure, such as diagonal tension or shear cracking.
- **Condition 2: The depth of the beam section is small, and the beam is loaded uniformly.**
A small depth (shallow beam) reduces the cross-sectional area, which lowers the shear capacity. However, under uniform loading, the maximum bending moment (at midspan) is typically more critical for shallow beams. This is because the bending stress is inversely proportional to the square of the depth (\( \sigma \propto 1/d^2 \)), making bending failure more likely than shear failure. Additionally, for uniformly loaded beams, the shear force is usually highest at supports but is often mitigated by support conditions, while bending dominates over most of the span. Therefore, this condition does not typically govern shear design.
Based on this analysis:
- Condition 1 alone causes the design to be governed by shear.
- Condition 2 does not cause the design to be governed by shear.
**Answer:** A) 1 only