The problem presents a simply supported beam with two point loads. The beam is supported at points A and C. A downward force of $60 \text{ kN}$ is applied at point B, which is $2 \text{ m}$ from A. A downward force of $30 \text{ kN}$ is applied at point D, which is $1 \text{ m}$ beyond point C. The reactions at A and C are $R_1 = 35 \text{ kN}$ and $R_2 = 55 \text{ kN}$, respectively. The shear force and bending moment diagrams are also provided. The question does not explicitly state what needs to be calculated. I will summarize key information from the diagrams.

Applied MathematicsStructural MechanicsBeam AnalysisShear Force DiagramBending Moment DiagramStatics
2025/5/15

1. Problem Description

The problem presents a simply supported beam with two point loads. The beam is supported at points A and C. A downward force of 60 kN60 \text{ kN} is applied at point B, which is 2 m2 \text{ m} from A. A downward force of 30 kN30 \text{ kN} is applied at point D, which is 1 m1 \text{ m} beyond point C. The reactions at A and C are R1=35 kNR_1 = 35 \text{ kN} and R2=55 kNR_2 = 55 \text{ kN}, respectively. The shear force and bending moment diagrams are also provided. The question does not explicitly state what needs to be calculated. I will summarize key information from the diagrams.

2. Solution Steps

From the shear diagram:
The shear force between A and B is 35 kN35 \text{ kN}.
The shear force between B and C is 25 kN-25 \text{ kN}.
The shear force between C and D is 30 kN30 \text{ kN}.
From the moment diagram:
The maximum positive moment occurs at B and is 70 kN-m70 \text{ kN-m}.
The moment at D is 30 kN-m-30 \text{ kN-m}.
The bending moment at A and C are both
0.

3. Final Answer

Maximum positive bending moment: 70 kN-m70 \text{ kN-m}
Bending moment at D: 30 kN-m-30 \text{ kN-m}

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