Q1: Dimensions of a beam need be changed if the shear stress is more than

ANS:C - 20 kg/cm²

The shear stress in a beam is a critical factor in its design, as it affects the beam's ability to resist applied loads and maintain structural integrity. When the shear stress in a beam exceeds certain limits, it can lead to shear failure, which is characterized by the development of diagonal cracks and eventual collapse of the beam. The maximum allowable shear stress in a beam depends on various factors, including the material properties, beam geometry, loading conditions, and design codes or standards. Generally, engineering standards such as those provided by the American Concrete Institute (ACI) or the American Institute of Steel Construction (AISC) specify maximum allowable shear stresses based on structural safety considerations. If the shear stress in a beam exceeds the maximum allowable limit specified by the relevant design code or standard, it indicates that the beam may be at risk of shear failure. In such cases, the dimensions of the beam may need to be changed to increase its shear capacity and ensure structural safety. Changing the dimensions of a beam to address excessive shear stress can involve various strategies, including:

1. Increasing the beam depth: Increasing the depth of the beam increases its moment of inertia, which enhances its ability to resist shear forces. This can be achieved by increasing the overall height of the beam or by increasing the height of specific components such as the web or flanges in the case of a steel beam.
2. Changing the beam cross-sectional shape: Modifying the cross-sectional shape of the beam can alter its shear resistance. For example, changing from a rectangular cross-section to a T-shaped or I-shaped cross-section can increase the beam's shear capacity by providing additional material away from the neutral axis, where shear stresses are highest.
3. Adding shear reinforcement: In reinforced concrete beams, shear reinforcement such as stirrups or shear links can be added to enhance the beam's shear capacity. Shear reinforcement helps to redistribute shear forces and prevent shear failure by providing additional resistance to diagonal cracking.
4. Using higher-strength materials: Using materials with higher tensile or shear strengths can increase the shear capacity of the beam without necessarily changing its dimensions. For example, using high-strength steel reinforcement in reinforced concrete beams or selecting structural steel with higher yield strength can improve the beam's overall shear resistance.
5. Modifying support conditions: Changing the support conditions of the beam, such as increasing the bearing area or providing additional lateral support, can help distribute shear forces more effectively and reduce shear stress concentrations.

Overall, when the shear stress in a beam exceeds allowable limits, it signals a potential structural vulnerability that must be addressed through appropriate design modifications. Changing the dimensions of the beam, along with other design strategies, can help mitigate the risk of shear failure and ensure the structural safety and integrity of the beam.