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QUESTION 1 STATICS 1.1 A beam ABCDE, 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 \( D \). (3) 1.1,3 Draw the bending moment and shearing force diagrams with the main values indicated on the diagram. (7)

Ask by Thornton Dawson. in South Africa
Mar 15,2025

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**Reaction Forces:** - \( R_A = 45 \, \text{N} \) - \( R_D = 47 \, \text{N} \) **Bending Moments:** - At \( B \): \( -90 \, \text{N m} \) - At \( C \): \( 56 \, \text{N m} \) - At \( D \): \( 34 \, \text{N m} \) **Shear Force Diagram:** - From \( A \) to \( B \): \( 45 \, \text{N} \) - At \( B \): \( -5 \, \text{N} \) - From \( B \) to \( D \): \( -5 \, \text{N} \) - At \( D \): \( 25 \, \text{N} \) - From \( D \) to \( E \): \( 13 \, \text{N} \) - At \( E \): \( -17 \, \text{N} \) **Bending Moment Diagram:** - At \( A \): \( 0 \, \text{N m} \) - At \( B \): \( -90 \, \text{N m} \) - At \( C \): \( 56 \, \text{N m} \) - At \( D \): \( 34 \, \text{N m} \) - At \( E \): \( 0 \, \text{N m} \) *Diagrams can be drawn based on these values to visualize the shear forces and bending moments along the beam.*

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Beyond the Answer

From a historical perspective, statics has its roots in classical mechanics, which was heavily influenced by the work of Sir Isaac Newton and his laws of motion in the 17th century. The study of forces and structures has evolved over centuries, enabling engineers to design safer, more efficient buildings and bridges. The principles of statics are foundational for various fields, from civil engineering to architecture, ensuring that structures can withstand loads and remain stable. In real-world applications, understanding statics is crucial for engineers when designing everything from household furniture to skyscrapers and bridges. Take a beam, like the one in your problem; engineers use statics to calculate reaction forces to determine how much weight it can support. Employing these principles allows for materials to be used effectively and prevents structural failures that can lead to costly repairs or safety hazards. So next time you marvel at a bridge or a building, remember the careful calculations that went into keeping it standing strong!

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