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STATICS QUESTION 1 \( \begin{array}{l}1.1 \text { A beam } A B C D E \text {, with } A \text { on the left-hand side, is } 10 \mathrm{~m} \text { long and simply supported at } \\ A \text { and } D \text {. Point loads of } 50 \mathrm{~N} \text { and } 30 \mathrm{~N} \text { are at } B \text { and } E \text { respectively. } A B=2 \mathrm{~m} \text { and } \\ D E=2 \mathrm{~m} \text {. } \\ \text { An evenly distributed load of } 2 \mathrm{~N} / \mathrm{m} \text { is between } A \text { and } D \text {. } \\ \begin{array}{l}1.1 .1 \text { First draw the beam, then calculate the reaction forces of } A \text { and } D \text {. } \\ 1.1 .2 \text { Calculate the bending moments at } B \text { and } D \text { and at a point } C \text { halfway between } \\ \text { (5 and } D \text {. } \\ \text { 1.1.3 Draw the bending moment and shearing force diagrams with the main values } \\ \text { indicated on the diagram. }\end{array}\end{array} \) (7)

Ask by Fuentes Macdonald. in South Africa
Mar 15,2025

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**Reaction Forces:** - \( R_A = 54.4 \, \text{N} \) - \( R_D = 37.6 \, \text{N} \) **Bending Moments:** - \( M_B = 108.8 \, \text{Nm} \) - \( M_C = 92 \, \text{Nm} \) - \( M_D = 0 \, \text{Nm} \) **Shear Force Diagram:** - From \( A \) to \( B \): \( +54.4 \, \text{N} \) - At \( B \): \( +4.4 \, \text{N} \) - From \( B \) to \( C \): \( +4.4 \, \text{N} \) - At \( C \): \( -7.6 \, \text{N} \) - From \( C \) to \( D \): \( -7.6 \, \text{N} \) - At \( D \): \( 0 \, \text{N} \) **Bending Moment Diagram:** - At \( A \): \( 0 \, \text{Nm} \) - At \( B \): \( 108.8 \, \text{Nm} \) - At \( C \): \( 92 \, \text{Nm} \) - At \( D \): \( 0 \, \text{Nm} \)

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To solve this problem, start by sketching the beam Diagram ABCDE to visualize the loading conditions. The support reactions at A and D can be determined using static equilibrium equations. First, calculate the total load: the point loads (50 N at B and 30 N at E) plus the total distributed load (2 N/m over 6 m, which equals 12 N). Use moments about point A or D to find the reactions R_A and R_D, which will provide insight into how the beam carries the loads. Next, compute the bending moments at key points including B and D, as well as point C, located halfway between A and D (5 m from A). To derive these moments, note that the bending moment varies due to the point loads and distributed load along the beam. For instance, at B, the moment is influenced solely by the load at E, while at D, it’s directly related to the reaction forces and point loads acting on the beam. Finally, draw the Shear Force and Bending Moment diagrams to visualize these internal forces acting within the beam. Indicate key values for clarity, as these diagrams are essential for further analysis in structural engineering!

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