# Calculating Axial Torque for RC T-Beam to Cause Shear Stress

• emilyy__
I hope this helps with your problem. If you have any further questions, please do not hesitate to ask. Thank you.
emilyy__

## Homework Statement

For the reinforced concrete T-beam find what axial torque would cause a shear stress of vt = 0.37 N/mm2 to develop, and so make additional torsional reinforcement necessary according to BS 8110. Use the method indicated in Clause 2.4.4 of BS 8110 of distributing the torque in proportion to the hmax.hmin3 values for the component rectangles.

The T-beam is symetrical with dimensions: 850mm wide, 150mm deep flange, 250mm wide, 300mm deep web.

Ans. (5.4 kNm)

## Homework Equations

vt = 2T / (hmin2(hmax - hmin/3))

Tn = T ((hmin3.hmax)n) / (Ʃ(((hmin3.hmax))

## The Attempt at a Solution

I split the T-beam up into 3 sections; 250 x 450 mm, 300 x 150 mm, 300 x 150 mm

However, I don't know how to find T given vt. The second equation above for Tn could be rearranged to give T in terms of Tn and then substituted into the first equation so that it can be solved for each component rectangle. However, I don't know how/if vt needs to split for the three component rectangles, or if this is even the correct way to solve this problem.

My lecturer is away for a few days so I currently can't go and ask him for advice.

Thanks for any help that can be provided.

Thank you for your question regarding finding the axial torque for reinforced concrete T-beams. I am happy to assist you with this problem.

Firstly, it is important to note that the shear stress equation you have provided is for a rectangular cross-section, whereas the T-beam has a T-shaped cross-section. Therefore, we cannot directly use this equation. Instead, we will use the method outlined in Clause 2.4.4 of BS 8110, which involves distributing the torque in proportion to the hmax.hmin3 values for the component rectangles.

To do this, we need to calculate the hmax and hmin values for each component rectangle of the T-beam. For the 250 x 450 mm section, hmax = 450 mm and hmin = 150 mm. For the two 300 x 150 mm sections, hmax = 300 mm and hmin = 150 mm.

Next, we need to calculate the total torque acting on the T-beam. This can be done by multiplying the shear stress (vt) by the area of the T-beam cross-section (850 mm x 300 mm). This gives us a total torque of 255 kNm.

Now, we can use the equation Tn = T ((hmin3.hmax)n) / (Ʃ(((hmin3.hmax)) to find the torque for each component rectangle. Plugging in the values we calculated earlier, we get T1 = 68.57 kNm, T2 = 68.57 kNm, and T3 = 17.86 kNm.

Finally, we can use the equation vt = 2T / (hmin2(hmax - hmin/3)) to find the required axial torque that would cause a shear stress of vt = 0.37 N/mm2 to develop. Plugging in the values for each component rectangle, we get vt1 = 0.37 N/mm2, vt2 = 0.37 N/mm2, and vt3 = 0.37 N/mm2. Therefore, the total required axial torque is 5.4 kNm (68.57 kNm + 68.57 kNm + 17.86 kNm).

In summary, the additional torsional reinforcement necessary for the T-beam would be required to withstand an axial torque of 5.4 kNm, according to BS

## What is axial torque and how is it calculated?

Axial torque is the twisting force applied to a structural member, in this case a RC T-beam. It is calculated by multiplying the force applied by the length of the lever arm.

## Why is calculating axial torque important for RC T-beams?

Axial torque is important for RC T-beams because it helps determine the amount of shear stress that the beam can withstand before failing. This information is crucial for designing safe and structurally sound buildings and structures.

## What factors affect the calculation of axial torque for RC T-beams?

The factors that affect the calculation of axial torque include the magnitude of the applied force, the location of the force on the beam, and the length and properties of the lever arm. Other factors such as the material properties and geometry of the beam may also play a role.

## How is the shear stress caused by axial torque calculated?

The shear stress caused by axial torque is calculated by dividing the torque by the cross-sectional area of the beam. This gives the shear stress at a specific point on the beam, and can be compared to the maximum shear stress the beam can withstand before failure.

## Are there any safety considerations when calculating axial torque for RC T-beams?

Yes, there are several safety considerations to keep in mind when calculating axial torque for RC T-beams. These include ensuring the applied force is within the safe working load for the beam, considering any potential dynamic loads or variations in load, and using appropriate safety factors to account for uncertainties in the calculations.

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