A laminated spring 1 m long is made up of plates, each 5 cm wide and 1 cm thick. If the bending stress in plates is limited to 100 MPa, how many plates would be required to enable the spring to carry a central point load of 2 kN. If E= 210 GPa, what is the deflection under the given load of 2 kN? Derive the formula used for deflection.

A laminated spring 1 m long is made up of plates, each 5 cm wide and 1 cm thick. If the bending stress in plates is limited to 100 MPa, how many plates would be required to enable the spring to carry a central point load of 2 kN. If E= 210 GPa, what is the deflection under the given load of 2 kN? Derive the formula used for deflection.

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter1: Tension, Compression, And Shear

Section: Chapter Questions

Problem 1.6.7P: A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The...

See similar textbooks

Similar questions

A wine of length L = 4 ft and diameter d = 0.125 in. is stretched by tensile forces P = 600 lb. The wire is made of a copper alloy having a stress-strain relationship that may be described mathematically by =18,0001+30000.03(=ksi) in which is nondimensional and has units of kips per square inch (ksi). (a) Construct a stress-strain diagram for the material. (bj Determine the elongation, of the wire due to the Forces P. (c) IF the forces are removed, what is the permanent set of the bar? (d) If the forces are applied again, what is the proportional limit?
A hollow copper pipe undergoes a 1% change in length under a tensile load. If the Young’s modulus of copper is 110 GPa, the pipe’s outer diameter is 2 cm and its wall thickness is 5 mm, what is the magnitude of the tensile load? Consider the whole change happening in the elastic region.
A bar having a circular cross section of 3 in. diameter is subjected to a torque of 100 in. # kip. If the material is elastic perfectly plastic, with tY = 16 ksi,determine the radius of the elastic core.
a machine mass m = 500 kg is mounted on a simply supported steel beam of length l = 2 that has a rectangular cross section (thickness = 0.1 m and width 1.2 m) and whose young modulus is given by E = 2.06x10 ^ 11 N / m2. To reduce the vertical deflection of the beam, a spring of stiffness k is added in the middle of the span, as shown in the following figure. Determine the value of k necessary to reduce the deflection of the beam by: a) -25% of its original valueb) -50% of its original valuec) -75% of its original value
A bar having a circular cross section is carrying a tensile load of 30 kN. If the diameter and length of the bar are 6 mm and 80 cm respectively, calculate the deflection. Assume Young’s modulus is 207 GPa
A 70kg human steps at the tip of a springboard used to dive in a pool. The springboard has a length of 1.75 meters, moment of inertia is 0.000002 m^4, and modulus of elasticity is 150 GPa. Determine the deflection of the springboard in millimeters. Note: δ=[(W)(L^3)]/[(3)(E)(I)] for a cantilever beam with end force.
the deflection of a beam whose length is 6 m with the modulus of elasticity of E = 200 GPa and I = 98.0 ✕ 106 mm4. The beam is designed to carry a load of 13,000 N/m. What is the maximum deflection of the beam (in m)? (Enter the y-value where the beam is deflected the most.)
For the simply supported beam carrying the concentrated load P = 268 N at its midspan, determine the magnitude of the maximum displacement (in mm) if d = 1.51 m, E = 11.77 GPa , and I =1679930mm4. NOTE: PLEASE ANSWER IT CORRECTLY. IF YOU ARE NOT SURE ABOUT THE ANSWER, PLEASE SKIP THE QUESTIONPLEASE BOX THE FINAL ANSWER(S)THANK YOU! image below for reference
A straight bar of uniform cross sectionis tested in tension. The bar's cross sectional is 6.5 square centimeters and a length of 4 m. When the tensile load reaches 85kN, the total elongation is 2.5mm. What is the stress and the modulus of elasticity of the bar?
The steel bar with a circular cross section of 14 mm diameter and 22 cm length, produced from a material with linear elastic behavior, elongates 0.11 mm under the effect of 16 kN tensile load and breaks at 24 kN load. How many MPa is the modulus of resilience of this bar?
1.) A 200 kg load is hung on a wire of length 4 m, cross sectional area of 0.2 x 10 -4 m2 and Young’s modulus of 8 x 1010 Pa. What is its increase in length? 2.) When a beam 6 m long with a cross-sectional area of 19.4 cm2 is subjected to a compression force of 16 x 104 N, its length is shortened by 4.5 mm. What is the Young’s Modulus for the beam?
– The weight is suspended from structural A–36 steel alloy and 2014-T6 aluminum alloy wires, eachhaving the same initial length of 10 ft and cross-sectional area of 7×10–3 in2 (Figure Q1). If the weight is increasedgradually, determine which wire yields first? Explain which material model and yield criterion you will use? Justifyyour choices