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consider a simply supported beam with a uniformly distributed load having a neutral axis (NA) as shown. For points P (on the neutral axis) and Q (at the bottom of the beam) the state of stress is best represented by which of the following pairs?

consider a simply supported beam with a uniformly distributed load having a neutral axis (NA) as shown. For points P (on the neutral axis) and Q (at the bottom of the beam) the state of stress is best represented by which of the following pairs? Correct Answer <img alt="F1 Shraddha Chandra 29.09.2021 D12" src="//storage.googleapis.com/tb-img/production/21/09/F1_Shraddha_Chandra_29.09.2021_D12.png" style="width: 176px; height: 44px;">

Explanation:

Given

[ alt="F1 Shraddha Chandra 29.09.2021 D15" src="//storage.googleapis.com/tb-img/production/21/09/F1_Shraddha_Chandra_29.09.2021_D15.png" style="width: 314px; height: 229px;">

We know the bending stress varies linearly.

Also Along the neutral axis, Bending stress is Zero.

Here as Mentioned Point (P) is at the Centre of  the span and also along the neutral axis

So, it is evident that @ P there is neither Shear force nor Bending stress

As shear force is Zero. There exists no shear stress at Point P

The state of stress can be shown as [ alt="F1 Shraddha Chandra 29.09.2021 D16" src="//storage.googleapis.com/tb-img/production/21/09/F1_Shraddha_Chandra_29.09.2021_D16.png" style="width: 42px; height: 42px;">

@ Point Q

As mentioned Point Q is on the bottom of the member which is subjected to Tension

As we know when the beam is subjected to downward loading the top portion of fibers (above NA) is subjected to Compression and the bottom fibers (Below NA) are subjected to tension.

At Point Q the Bending stress is maximum (Tension side). Shear Force at Pont Q is also Zero.

So State of stress at point Q can be shown as [ alt="F1 Shraddha Chandra 29.09.2021 D17" src="//storage.googleapis.com/tb-img/production/21/09/F1_Shraddha_Chandra_29.09.2021_D17.png" style="width: 108px; height: 41px;">

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