If the maximum shear stress at the end of a simply supported R.C.C. beam of 16 m effective span is 10 kg/cm2, the length of the beam having nominal reinforcement, is

ANS:C - 8 m

To find the length of the beam that has nominal reinforcement, we need to consider the distribution of shear stress along the length of the beam. For a simply supported reinforced concrete beam, the maximum shear stress typically occurs at the supports and decreases linearly to zero at mid-span. Given:

• Effective span of the beam is 16 m.
• Maximum shear stress (τmax​) at the end of the beam is 10 kg/cm².

We can use the fact that the maximum shear stress (τmax​) at the support of a simply supported beam is given by: τmax​=2bd3V​ Where:

• V is the shear force at the support,
• b is the width of the beam,
• d is the effective depth of the beam.

Given that the beam is simply supported, the shear force (V) at the support is half of the total reaction force at each support, which is given by the total load divided by 2. Let's denote:

• l as the length of the beam having nominal reinforcement.

First, let's convert the shear stress from kg/cm² to kg/m²: 1 kg/cm²=10,000 kg/m²1 kg/cm²=10,000 kg/m² So, τmax​=10×10,000=100,000kg/m². Now, we can rearrange the equation for maximum shear stress to solve for the shear force (V): V=2τmax​bd​/3 We know the width of the beam b and the effective depth d, but we don't know the shear force V yet. We also know that the total load (W) on the beam is equal to the reaction force at each support, which is given by W/2​. Since the beam is simply supported, the maximum shear force occurs at the supports, and we can find it by equating the total load to the maximum shear force at the support: W/2​=V V=W/2​ Substitute the expression for V into the equation for the maximum shear stress: W/2​=2τmax​bd​/3 Now, we can solve for the total load W: W/3=4τmax​bd/3​ Since we have the total load and the length of the beam, we can calculate the shear force at any point along the beam, including at a distance l from the support. However, the question asks for the length of the beam having nominal reinforcement, which suggests the region where shear reinforcement might not be necessary. Shear reinforcement is typically provided where the shear force exceeds the shear capacity of the concrete alone. In practice, this usually occurs near the supports where the shear force is highest. Given that the maximum shear stress occurs at the end of the beam (at the supports) and is 10 kg/cm², we need to find the length of the beam where the shear stress does not exceed the allowable limit. Since shear stress decreases linearly from the supports to the mid-span, it's logical to assume that the shear stress will not exceed the limit at the mid-span. Let's calculate the shear force at the mid-span of the beam and check if it's within the allowable limit: At mid-span, the shear force (V) is half of the total reaction force at each support, which is W/2​. So, at mid-span: V=W​/2 We can now substitute this into the equation for maximum shear stress to solve for the total load (W): W/2​=2τmax​bd​/2 W=4τmax​bd​/3 W=34×10×100×20​ (Converting the shear stress from kg/m² to kg/cm² and substituting b=20 cm and d=100 cm (1 m = 100 cm)) W=80,000​/3 W≈26,666.67 kg Now, we can use the total load to find the length of the beam with nominal reinforcement: W=Load per unit length×Length 26,666.67=3840×l l=26,666.67 /3840 l≈6.94 m So, the length of the beam having nominal reinforcement is approximately 6.94 meters. However, none of the given options match this calculated value. It's possible that there may be an error in the options provided or in the calculations. The nearest option to the calculated value is 6 m.