Determination of Bending's Modulus PDF

(5) Determination of the Bending's Modulus Objective: determination of Bending's modulus (or Flexural modulus) Theory:  Consider a bar AB supported on knife edges, and is loaded in the middle The bar is depressed in the middle by amount h given by:...

(5) Determination of the Bending's Modulus Objective: determination of Bending's modulus (or Flexural modulus) Theory:  Consider a bar AB supported on knife edges, and is loaded in the middle The bar is depressed in the middle by amount h given by: 𝑔𝐿3 ∆ℎ = 𝑚 4𝑏𝑑 3 𝐸𝐵 Where; (𝐿) the length of the bar (𝑏) the width of the bar (𝑑) the thickness of the bar (𝐸𝐵 ) Bending's modulus (𝑚) the mass  The relation between (∆ℎ) and (𝑚) is a straight line passes through the origin and have slope= 𝑔𝐿3 4𝑏𝑑 3 𝐸𝐵 Apparatus: Metal bar, two knife edges, set of weights, vernier caliper Method: At constant length: 1. Measure the dimensions of the bar (𝐿), (𝑏) and (𝑑) 2. Put the pan in the middle and record the zero-reading (ℎ0 ) 3. Put a weight in the pan and record the displacement (∆ℎ) 4. Increase the weight and record the displacement 5. Plot a relation between (∆ℎ) and (𝑚) and determine (𝐸𝐵 ) h (cm) m (gm) Results: 𝑏 = ⋯ 𝑐𝑚, 𝑑 = ⋯ 𝑐𝑚 𝑎𝑛𝑑 𝐿 = ⋯ 𝑐𝑚 ℎ0 = … 𝑐𝑚 𝑚 (𝑔𝑚) ℎ+ (𝑐𝑚) ∆ℎ (𝑐𝑚) 𝐸𝐵 =