To determine The maximum height h from which the 50-kg block can be dropped without cause yielding in the cantilever beam. Explanation Given information: The weight of the block dropped is 50 kg. The beam is made from A992 steel and is a W 200 × 46 wide-flange section. Consideration: The Young’s modulus or modulus of elasticity of the A992 steel is E = 200 × 10 9 N/m 2 . The acceleration due to gravity is g = 9.81 m/sec 2 . The maximum allowable bending stress is σ Y = 345 MPa . Refer to Appendix B ‘Geometric Properties of Structural shapes’ in the textbook. Take the properties of W 200 × 46 beam as follows: The moment of inertia of the beam is I = 45.5 × 10 6 mm 4 and The depth of the beam is d = 203 mm . Refer to Appendix C, ‘Slopes and Deflections of beams’ in the textbook. Show the deflection for the cantilevered beam when the load is applied at free end. Δ s t = P L 3 3 E I (1) Here, Δ s t is static displacement. P is load applied on the beam, L is length of the beam up-to mid-span from fixed end, E is Young’s Modulus, and I is moment of inertia. Weight of the block: Determine the weight of the block using the relation. P = m g (2) Here, m is mass of the block and g is acceleration due to gravity. Substitute 50 kg for m and 9.81 m/sec 2 for g in Equation (2). P = 50 × 9.81 = 490.5 N Substitute 490.5 N for P , 3 m for L , 200 × 10 9 N/m 2 for E , and 45.5 × 10 6 mm 4 for I in Equation (1). Δ s t = 490.5 × 3 3 3 × 200 × 10 9 × 45.5 × 10 6 mm 4 × 1 m 4 ( 1 , 000 mm ) 4 = 0.48511 × 10 − 3 m Maximum dynamic force: Determine the maximum dynamic force using the formula. P max = n P (3) Substitute 490.5 N for P in Equation (3). P max = n × 490.5 = 490.5 n Moment at the point A : Determine the moment at fixed end A using the relation

9th Edition

ISBN: 9780133254426

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Videos

Question

Chapter 14.4, Problem 14.65P

To determine

The maximum height h from which the 50-kg block can be dropped without cause yielding in the cantilever beam.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 14.64P

Chapter 14.4, Problem 14.66P

Students have asked these similar questions

A converging elbow (see the figure below) turns water through an angle of 135° in a vertical plane. The flow cross section diameter is 400 mm at the elbow inlet, section (1), and 200 mm at the elbow outlet, section (2). The elbow flow passage volume is 0.2 m³ between sections (1) and (2). The water volume flowrate is 0.1 m³/s and the elbow inlet and outlet pressures are 140 kPa and 90 kPa. The elbow mass is 11 kg. Calculate the (a) horizontal (x direction) and (b) vertical (z direction) anchoring forces required to hold the elbow in place. D₂- Section (1)- D₁ = 400 mm 135° 200 mm Section (2) (a) Fx= i 20809.96 N (b) Fz= i -120265 N

2: A rectangular aluminum block is loaded uniformly in three directions. The loadings are as follows:a 50 kN total resulting compressive load in the x-direction, a 200 kPa uniformly distributed tensile load in they-direction, and a 0.03 MN total resulting tensile load in the z-direction. The block has the following dimensions:L = 1 m, b = 20 cm, h = 350 mm. Use E = 70 GPa and ν = 0.25.Determine the strain in the x and y axes respectively. For the strain in the y-direction to be equal to 0, how much uniformly distributed load inthe surface of y-direction should be added? (+ for tensile, - for compressive) Answers: 5 -1.122 x10-5 / 3 decimals 6 5.102 x10-6 / 3 decimals 7 -0.357 MPa / 3 decimals

A spherical balloon with a diameter of 9 m is filled with water vapour at 200˚C and 200 kPa. Determine the mass of water in the balloon. The R value for water is 0.4615 kJ/kg∙K.

Chapter 14 Solutions

Mechanics of Materials

Ch. 14.2 - A material is subjected to a general state of...Ch. 14.2 - The strain-energy density for plane stress must be...Ch. 14.2 - 14–3. Determine the strain energy in the stepped...Ch. 14.2 - Prob. 14.4P Ch. 14.2 - Using bolts of the same material and...Ch. 14.2 - If P = 60 kN, determine the total strain energy...Ch. 14.2 - Determine the maximum force P and the...Ch. 14.2 - *14–8. Determine the torsional strain energy in...Ch. 14.2 - Determine the torsional strain energy in the A-36...Ch. 14.2 - The shaft assembly is fixed at C. The hollow...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.