A simply supported beam AB has a clear span of 7 meter. The bending moment diagram (BMD) of the beam due to a single concentrated load is shown in the figure below.
The magnitude of the concentrated load in kN is __________.
To determine the magnitude of the concentrated load on the beam, we will use the maximum bending moment formula for a simply supported beam with a point load:
M = P × a × b / L
Where:
- M is the maximum bending moment (36 kN-m as shown in the figure).
- P is the concentrated load (unknown, in kN).
- a and b are the distances from the supports to the point of load application (3 m and 4 m respectively).
- L is the total span of the beam (7 m).
Rearranging the formula to solve for P:
P = M × L / (a × b)
Substitute the known values:
P = 36 kN-m × 7 m / (3 m × 4 m)
P = 252 kN-m / 12 m
P = 21 kN
The magnitude of the concentrated load is 21 kN. This value falls within the expected range of 21 to 21 kN, confirming the correctness of our solution.
Important Questions from Strength of Materials
- A simply-supported steel beam made of an I-section has a span of $8 \text{ m}$. The beam is carrying a uniformly distributed load of $15 \text{ kN/m}$. The overall depth of the beam is $450 \text{ mm}$. The moment of inertia of the beam section is $18000$ cm$^4$. The maximum bending stress in the beam will be _________ N/mm$^2$. [in integer]
A simply supported RCC beam of cross section $0.4 \text{ m} \times 0.6 \text{ m}$ covers a span of $8 \text{ m}$. It is subjected to a uniformly distributed load of $30 \text{ kN/m}$. If the unit weight of concrete is $24 \text{ kN/m}^3$, the tensile stress (in $N/mm^2$, rounded off to two decimal places) at the bottom of the beam at mid-span is______
A rectangular beam section of size 300 mm (width) X 500 mm (depth) is loaded with a shear force of 600 kN. The maximum shear stress on the section in N/mm² is ___________
- A steel I-beam section is subjected to a bending moment of 96 kN-m. The moment of inertia of the beam section is $24,000 \text{ cm}^4$. The bending stress at 100 mm above the neutral axis of the beam in MPa will be ________
- A load of 30 kN is applied vertically downward at the free end of a cantilever of span 5 m. If the elastic modulus of the cantilever is 30 GPa and the section has a width of 0.3 m and a depth of 0.6 m, then, the elastic deflection (in mm) is ________
