JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech II Year STRUCTURAL ANALYSIS Previous Question Paper (November/December - 2020 - R16)

To analyze the propped cantilever beam of length L = 8 m with a point load P = 70 kN at a distance a = 3 m from the fixed end, we treat the prop at the free end as a redundant reaction R_B.

Using the principle of superposition or the compatibility equation (deflection at the prop = 0):

Substituting the values L = 8, a = 3, and P = 70:

Now, calculate the reaction at the fixed end (R_A):

The Shear Force Diagram (SFD) is constructed as follows:

• From x = 0 to 3 m: The shear force is constant at +57.08 kN.
• At x = 3 m: The shear force drops by the point load of 70 kN to 57.08 - 70 = -12.92 kN.
• From x = 3 m to 8 m: The shear force remains constant at -12.92 kN.
• At x = 8 m: The shear force returns to zero due to the upward reaction R_B = +12.92 kN.

For a fixed beam of length L subjected to a central point load W, the beam is statically indeterminate to the second degree. Due to symmetry, the vertical reactions at both supports are equal to W/2. The fixed end moments at both supports are equal to WL/8.

The Shear Force (SF) values are determined as follows:

1. At the left support (x = 0), the shear force is +W/2.
2. Between the left support and the center (0 < x < L/2), the shear force remains constant at +W/2.
3. At the center (x = L/2), the shear force changes abruptly from +W/2 to -W/2 due to the downward point load W.
4. Between the center and the right support (L/2 < x < L), the shear force remains constant at -W/2.
5. At the right support (x = L), the shear force is -W/2.

The Shear Force Diagram (SFD) is a rectangular plot. It starts at +W/2 at the left support, stays constant until the mid-point, drops vertically by W at the center to reach -W/2, remains constant until the right support, and finally closes back to zero at the right support.