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QUESTION 1 STATICS 1.1 A bearn \( A B C D E \), with \( A \) on the left-hand side, is 10 m long and simply supported at \( A \) and \( D \). Point loads of 50 N and 30 N are at \( B \) and \( E \) respectively. \( A B=2 \mathrm{~m} \) and \( D E=2 \mathrm{~m} \) An evenly distributed load of \( 2 \mathrm{~N} / \mathrm{m} \) is between \( A \) and \( D \). 1.1.1 First draw the beam, then calculate the reaction forces of \( A \) and \( D \). (5) 1.1.2 Calculate the bending moments at \( B \) and \( D \) and at a point \( C \) halfway between B and D. 1.1.3 Draw the bending moment and shearing force diagrams with the main values indicated on the diagram. \( 1.2 \quad y \)-axis

Ask by Chambers Colon. 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:** - At \( B \): \( 108.8 \, \text{N m} \) - At \( C \) (midpoint between \( B \) and \( D \)): \( 93.6 \, \text{N m} \) - At \( D \): \( 168 \, \text{N m} \) **Shearing Force Diagram:** Starts at \( 54.4 \, \text{N} \), drops by \( 50 \, \text{N} \) at \( B \), further drops by \( 12 \, \text{N} \) due to UDL, drops by \( 30 \, \text{N} \) at \( E \), and ends at \( 37.6 \, \text{N} \). **Bending Moment Diagram:** Starts at \( 0 \) at \( A \), increases to \( 108.8 \, \text{N m} \) at \( B \), decreases to \( 93.6 \, \text{N m} \) at \( C \), increases to \( 168 \, \text{N m} \) at \( D \), and ends at \( 0 \) at \( E \).

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The static equilibrium of beams dates back to the ancient Greeks, who laid the mathematical foundations still used today. Concepts like moments and shear forces were explored by pioneers such as Archimedes and later expanded by mathematicians during the Renaissance. By the time modern engineering arose, the principles had evolved significantly, becoming essential in designing bridges, buildings, and other structures. In the real world, understanding beam reactions and internal forces is crucial for safe and effective engineering designs. From constructing skyscrapers to designing everyday items like bookshelves, engineers rely on static analysis to ensure that structures can withstand applied loads without failure. It’s all about keeping everything balanced while avoiding potential hazards!

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