Q1: If T and R are the tread and rise of a stair which carries a load w per square metre on slope, the corresponding load per square metre of the horizontal area, is

ANS:B -

To determine the corresponding load per square meter of the horizontal area for a stair that carries a load w per square meter on the slope, we need to consider the geometry of the stair and the distribution of the load. Let's denote:

• T as the tread (horizontal depth) of the stair,
• R as the rise (vertical height) of the stair,
• θ as the angle of inclination of the stair with respect to the horizontal,
• w as the load per square meter on the slope.

First, we need to find the length of the slope (hypotenuse of the stair). This can be calculated using the Pythagorean theorem: Length of slope=T^2+R^2​ The horizontal projection of this length is equal to the tread T. So, the load per square meter on the horizontal area can be found by dividing the load per square meter on the slope by the horizontal projection of the length: Load per square meter on horizontal area =w⋅T/Length of slope ​ Given that Length of slope=T^2+R^2​, the formula for the load per square meter on the horizontal area becomes: Load per square meter on horizontal area=w⋅T/T^2+R^2​​ This formula provides the load per square meter of the horizontal area for a stair that carries a load w per square meter on the slope.