A 4 m simply supported beam has a rectangular cross-section of 100 mm by 50 mm. The second moment of area is 4.17×10^6 mm^4, and the maximum allowable bending stress at the bottom edge is 42 MPa. A point load $$F$$ is applied at the midspan. What is the maximum permissible value of $$F$$ ?

A cantilever beam must withstand a maximum bending moment of 750 N·m. Five candidate sections have the following Ix (m⁴) and ymax (m): A: Ix= $$1.688\times10^{-6}$$ , ymax=0.050; B: Ix= $$1.412\times10^{-6}$$ , ymax=0.040; C: Ix= $$2.459\times10^{-6}$$ , ymax=0.065; D: Ix= $$0.916\times10^{-6}$$ , ymax=0.035; E: Ix= $$1.269\times10^{-6}$$ , ymax=0.040. Select the section that minimizes maximum bending stress $$\sigma_{max} = \frac{M \cdot ymax}{Ix}$$ , and estimate $$\sigma_{max}$$ for that section.

A simply supported beam spans 3.0 m between two pinned supports. A point load is applied at midspan, producing a peak bending moment of 750 N·m at the center and zero at the supports. What is the reaction force at each support?

A simply supported cross-beam carries four concentrated downward loads: 6 kN at 0 m, 5 kN at 1 m, 5 kN at 3 m, and 4 kN at 5 m from the left end. On the shear force diagram, what happens to the shear value immediately after passing the 1 m point?

Two beams A and B carry the same bending moment M. Beam A is an I-section and Beam B is a solid rectangle of the same overall depth. Which statement best explains why the maximum bending stress is lower in beam A? Use σ = My/I.

A rectangular hole must be cut in a simply supported steel beam to pass a service pipe. Three possible positions are shown: A at the mid‑depth near the center web, B as a recess at the bottom edge, and C near the top edge. Which location minimizes the reduction in bending strength?

A simply supported beam carries two downward point loads: 8.0 kN at 3.5 m from the left support and 12.0 kN at 6.5 m from the left support. The reactions are 9.4 kN at the left support and 10.6 kN at the right support. Which bending moment diagram best represents the beam, given that the bending moment is Varignon-consistent, starts and ends at zero, increases linearly between loads, and shows maximum positive ordinates near the loads of approximately 32.9 kNm and 37.1 kNm?

A simply supported 3 m beam carries a 20 kN point load at midspan. Four candidate cross-sections have the same area A = 350 mm² and y_max = 150 mm, but different second moments of area: A: $$0.8\times10^6 mm^4$$ , B: $$72.0\times10^6 mm^4$$ , C: $$94.3\times10^6 mm^4$$ , D: $$120.7\times10^6 mm^4$$ . Which section minimizes the maximum bending stress?

A 2 m forklift beam is simply supported with reactions at the left and right forks. A 9 kN point load acts 0.8 m from the left support and 1.2 m from the right support. What is the vertical reaction at the right support?

A simply supported beam carries a uniformly distributed load (including self‑weight) over its entire span. Which statement best describes the typical shapes of the shear force and bending moment diagrams?

A simply supported concrete beam carries three point loads: 30 kN at 2 m from the left support, 20 kN at 5 m from the left support, and 10 kN at 8 m from the left support. What is the reaction at the right support?

A simply supported plank beam spans 5 m and carries two point loads representing workmen: 900 N at 1 m from the left support and 1000 N at 2 m from the left support. What is the vertical reaction at the right support RB?

Which statement best describes shear force and bending moments in a beam?

A simply supported 2 m cross beam carries two point loads: 900 N at 0.4 m from the left support and 600 N at 1.6 m from the left support. Ignoring self-weight, which sketch best represents the qualitative shape of the bending moment diagram (BMD)?

When a uniformly distributed load (UDL) is added to a simply supported beam previously analyzed with only point loads, how does the shape of the bending moment diagram (BMD) change between supports?

A beam cross-section has second moment of area I = $$14 \times 10^{-6} m^4$$ . At a section where the bending moment is M = $$336 N\cdot m$$ and the distance to the outer fiber is y = $$0.075 m$$ , estimate the maximum bending stress using $$\sigma = \frac{My}{I}$$ .

A simply supported 16 m beam carries two equal point loads of 5 kN located 5 m from the left support and 5 m from the right support. What is the reaction at each support?

For the same 16 m beam with two 5 kN point loads placed symmetrically as described, what is the maximum bending moment in the beam?