Find the stiffness of each spring and the stiffest spring.
Answer to Problem 1P
The stiffness of each spring is
Explanation of Solution
Formula used:
Formula used to calculate the spring force is,
Here,
Calculation:
Refer to figure Problem 18.1 in textbook, the graph with force-deflection relationships for three springs A, B and C are given.
Rearrange equation (1) to find
Refer to Figure Problem 18.1 in textbook,
For spring A,
At
For spring B,
At
For spring C,
At
Substitute
Substitute
Substitute
Comparing the values in equation (3), (4) and (5), the spring B is the stiffest spring.
Therefore, the stiffness of each spring is
Conclusion:
Thus, the stiffness of each spring is
Want to see more full solutions like this?
Chapter 18 Solutions
ENGINEERING FUNDAMENTALS
- Suppose we have a uniform beam that is 3.73 metres long has a flexural rigidity of 34301Nm. Find the deflection of the beam in millimetres if the beam is under a uniform load of 86N/m and is supported with simple supports at both ends. Fill out the table below with your answers. x�-coordinate Deflection (mm��) x=0.22 y(x)= x=1.38 y(x) = x=2.05 y(x) = x=2.98 y(x) = x=3.58 y(x) = Enter as many decimal places as your calculator allows (8 to 10). Your answer must be within ±0.0005±0.0005 of the correct answer to be considered correct.arrow_forward3) Nails are used to connect three boards to form a beam as shown in the figure. Each nail has a shear strength of 40ON. The beam is subjected to a vertical shear. Geometrical details are given in the figure. Calculate the allowable shear force for this beam. (Suggested time for solution is 25 mimutes) 75mm 75mm 75mim 60 mm 120mm, 60 mm 60 mm 200 mmarrow_forwardGiven that the three bars shown in the accompanying figure are made of the same material, comparing bar (a) to bar (b) which bar will stretch more, when subjected to the same force F ? Bar (a) and (b) have the same cross-sectional area but different lengths. Comparing bar (a) to bar (c) having the same length but different cross-sectional areas, which bar will stretch more? Explain.arrow_forward
- A long rectangular copper bar under a tensile load P hangs from a pin that is supported by two steel posts as shown in figure below. The copper bar has a length of 2.0 m, a rectangular cross section of 20 mm x 200 mm, and a modulus of elasticity Ecu = 100 GPa. Each steel post has a height of 0.5 m, a rectangular cross section of 20 mm x 250 mm, and a modulus of elasticity Es = 200 GPa. Steel post A Copper bar a.) Determine the downward displacement 8 of the lower end of the copper bar with respect to the base support of the steel post at point A due to a load P = 150 kN. (20 marks) b.) What is the maximum permissible load Pmax if the displacement d is limited to 1.0 mm? (5 marks) тазarrow_forwardA stiff bar of negligible weight transfers a load P to a combination of three helical springs arranged in parallel as shown in the figure below. The springs are made up of the same materials and out of rods of equal diameters. They are of same free length before loading. The number of turns in those three springs are 10, 14 and 18 respectively, while the mean diameters are in the ratio 1.0 : 1.5 : 2.0 respectively. Find the distance "x" such that the bar remains horizontal after the application of the load P. 6 ft 6 ftarrow_forwardAn engineering company approaches you and asks you to model the mechanical stresses on a magnet that is being used in an electronic storage device. The company wants you to calculate the stresses over a grid of small boxes covering the magnet's surface, where each box has dimensions 3 um by 3 um. Assume that the magnet is never in motion. Can the continuum approximation be accurately applied to this problem? Why or why not?arrow_forward
- The figure shows the infinitely rigid bar (ACD) suspended by three steel wires of diameter d and elasticity E σy, whose maximum allowable stress in the elastic range is σy. On the bar, weighing W, it also exerts a point force P as indicated in the figure. W= 10 [kN], P=5 [kN], d=5 [mm], L=1 [m], b=50 [cm], E=190 [GPa] , σy= 200 [MPa]. a) Calculate the vertical reactions on each of the wires.If applicable, indicate what wires are at risk of collapse b) Calculate the deformations of each wire for the case shown in a) c) Calculate the maximum deformations in each wire so that their behavior remains in the elastic rangearrow_forwardGiven a cantilever beam with given loadings and cross-section as shown in the figures, what is the second moment of area ( moment of inertia) of the diamond cross-section? (in mm^2) write the answer in ordinary notationarrow_forwardA system of forces is acting on a rectangular plate, as shown in the figure below. The direction of the resultant force * with x-axis is j100 N A 50 N 3 m 40 N D 5 m 70 N 86.6 degrees 273.4 degrees 68.8 degrees none of the abovearrow_forward
- Part D - Analyzing a system of forces acting on a concrete slab The concrete slab shown in the picture is subject to four forces, F1=125 lb, F2=260 lb, F3=675 lb, and F4=255 lb. (Figure 3) The dimensions are d1=8.0 ft, d2=24 ft, d3=3.0 ft, d4=13 ft, and d5=9.5 ft. Determine the equivalent resultant force by specifying its magnitude and its location (x,y) on the slab. Express your answers, separated by commas, to three significant figures. FR, x, y= lb, ft,ftarrow_forwardTwo beams are connected by a linear spring as shown in the following figure. For a Load P as shown in the figure, the percentage of the applied load P carried by the spring isarrow_forward1. State in words the condition for rotational equilibrium. 2. In exercise physiology studies, it is sometimes important to determine the location of a person's center of gravity. This can be done with the arrangement shown in the figure below. A light plank rests on two scales that read Fg1 = 380 N and Fg2 = 320 N. The scales are separated by a distance of 2.00 m. How far from the woman's feet is her center of gravity? -2.00 m JOH Fgl Hal Fg2\arrow_forward
- Engineering Fundamentals: An Introduction to Engi...Civil EngineeringISBN:9781305084766Author:Saeed MoaveniPublisher:Cengage Learning