An overhead crane can be modelled as the beam system shown in Figure Q3. The beam of length L = 2.6 m is made of steel with Young's modulus, E = 202.4 x 10⁹ N/m². The secon moment of area of the beam 1 = 3.7 x 10-4 m². The stiffness of the spring, k₁ = 6.2 x 10³ N/m. The mass due to the load being lifted, m₁ = 3.4 x 10² kg. The beam mass is negligible compared with the load. You are required to find the equivalent stiffness of the beam, and then as your answer, to find the natural frequency of the system in Hz. Fill this answer in the box below. (Express your answer to 2dp) Flg. Q3 Answer: m₁ k₁

An overhead crane can be modelled as the beam system shown in Figure Q3. The beam of length L = 2.6 m is made of steel with Young's modulus, E = 202.4 x 10⁹ N/m². The secon moment of area of the beam 1 = 3.7 x 10-4 m². The stiffness of the spring, k₁ = 6.2 x 10³ N/m. The mass due to the load being lifted, m₁ = 3.4 x 10² kg. The beam mass is negligible compared with the load. You are required to find the equivalent stiffness of the beam, and then as your answer, to find the natural frequency of the system in Hz. Fill this answer in the box below. (Express your answer to 2dp) Flg. Q3 Answer: m₁ k₁

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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An overhead crane can be modelled as the beam system shown in Figure Q3. The beam of length L = 7.2 m is made of steel with Young's modulus, E = 183.7 x 10⁹ N/m². The second moment of area of the beam 1 = 5.4 x 10-4 m². The stiffness of the spring, k₁ = 1.9 x 10³ N/m. The mass due to the load being lifted, m₁ = 4.3 x 10² kg. The beam mass is negligible compared with the load. You are required to find the equivalent stiffness of the beam, and then as your answer, to find the natural frequency of the system in Hz. Fill this answer in the box below. (Express your answer to 2dp) Flg. Q3 Answer: 43.11 ww k₁
(а) Draw the free-body diagram of the truss. (b) Calculate the reaction forces at the supports. (c) Calculate the member forces FAB, FBc and FAC and state if they are in tension or compression.
Figure 1.29 shows the suspension system of a freight truck with a parallel-spring arrangement. Find the equivalent spring constant of the suspension if each of the three helical springs is made of steel with a shear modulus G = 100 GPaand has 10 effective turns, mean coil diameter D = 50 cm, and wire diameter d = 5 cm
The 2- dimensional truss shown in FIGURE Q2 is made of material that has a modules of elasticity E = 150x10° N/m². The cross sectional area of each member is 0.01 m?. Forces P, and P2 are acting as shown, Wall (a) (b) 40% (c)/30 P' P= 2kN 4m FIGURE Q2 a. You are required to design TWO (2) different system's fixing type of nodes 2, 3, and 4 to the wall. Then recommend the best option that provides the lowest displacement at node 1 by performing complete calculations to justify your recommendation. b. After the client approved your recommendation in (a), it was found that the displacements occurred at node 1 is still high. As a result, you are required to modify the truss design in order to reduce the displacement at node 1 by minimum 15% on a condition that modules of elasticity, and the force remain unchanged. Justify your recommendation. Las digit in Student ID O to 3 4 to 6 7 to 9 30° 36° 40° PI 5 kN 7 kN 8 kN
For this problem, take a look at Figure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y = 0, and the spring is in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. k Schen a 0 a F The equation of motion for the system can be derived to be: a 4aM0+ ak0 =-F-2Mg T y M Your tasks: A. Transform the rotational equation of motion, which is in 0, given above, to another variable, y, which is zero at the static equilibrium position. onical system in sta bace form. Using MATLAB or a calculator lues of INI. W 16 [N/m], and C. Derive the response of the system in the Laplace (s) domain. Use the static equilibrium value found in part A (Ost) as the initial value, (0), for the problem. Assume (0) and the force, F, are both zero. You may treat gravity as g = 10 [m/s²] for ease of…
Figure Q1(a) shows a fire truck system which consist of a bucket attached at the end of the telescoping arm. Given that the mass of the bucket including the fireman is W = 300 kg, the length of the telescoping arm given as l1= l2= 13= 10 m, with cross- sectional areas of A1= 40 cm?, A2= 20 cm² and A3= 5 cm? and Young's modulus, E = 2.5 x 1011 Pa. Q1 (a) (i) Analyze the total stiffness of the telescoping arm in a vertical direction. (ii) Determine the natural frequency of the system.
Three springs with different spring constants are connected as shown below. You are going to use spring elements to simulate this system. Suppose that the spring constants of the first, second and third elements are k1=3,410 N/m, k2=3,160 N/m and k3=3,380 N/m, respectively. Two horizontal forces are applied to the system (as shown) at nodes. 2 and 3. Find the displacement of node 3 and write your answer in mm (millimetre). Hint: Write your answer with 5 decimal places. For example if you calculated the value 1.2345678, then rounding off to 5 decimal places yields 1.23457 and that is the value you need to type in the answer box. U₁=0 (1) F₂ = 2N U₂ = ? F3 = -1N (2) M U3 = ? (3) U4 = 0
For this problem, take a look at Figure 2. Assume that the rod is massless, perfectly rigid, and pivoted at point P. When the rod is perfectly horizontal, the angle 0 = 0, the displacement y = 0, and the spring is in neither tension nor compression. Gravity acts on the system (e.g. on mass M). We assume that y is a small displacement. A mass M is attached at the end of the rod. k Schen a 0 a F The equation of motion for the system can be derived to be: a 4aM0+ ak0 =-F-2Mg T y M Your tasks: A. Transform the rotational equation of motion, which is in 0, given above, to another variable, y, which is zero at the static equilibrium position. B. Represent the mechanical system in state space form. Using MATLAB or a calculator (just say what you used), calculate the eigenvalues of your A matrix for the following system parameters: a = 0.25 [m], M = 1 [kg], k = 16 [N/m], and F = 0 [N]. What do the eigenvalues say about the stability of the system? C. Derive the response of the system in the…
Truck suspensions often have "helper springs" that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in the figure below. When the main leaf spring is compressed by distance yo, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 5.15 x 105 N/m, the helper spring constant is 3.80 x 105 N/m, and y₁ = 0.500 m. m Need Help? Truck body Main leaf spring (a) What is the compression of the leaf spring for a load of 4.90 x 105 N? Read It -"Helper" spring Axle (b) How much work is done in compressing the springs?
3. 2 ft 1106 2 ft B ww Cord AB is 2 ft long, the force P = 76 lb, the angle 0 = 56 degrees and the spring's stiffness is k = 56 Ib/ft.
A wooden beam is loaded by a distributed load =5 N/mm as shown in Figure Q4(a). The cross-section of the beam is shown in Figure Q4(b). Assume that LAB=1700 mm, Lục = 3300 mm, W=180 mm, By = 20 mm, and H = 210 mm, ha-20 mm. Units: use N, mm, MPa as consistent units for all calculations. Decimal points: any decimal points are fine and all the numerical questions have a 10% error tolerance. Steps: Fill the gaps in the "steps" to get some marks from the working out process. Adaptive marking is still used. (a) (b) hoi Bo Lan Cross-section Figure Q4: (a) A wooden beam is loaded by a distributed load, (b) cross-section of the beam. b) Calculate support reactions in A and C, remember the sign of the force. Reaction force at point A: x direction: X4= N, y-direction: Y= Reaction force at point C: xdirection: Xe N, y direction: Ye
3 Q2 A beam, AB, of weight W= 50 N and length L = 0.8 m is supported by two springs, as shown in figure 2.1. The two springs have identical unstressed length; the spring on the left has a spring constant, k, = 200 N/m, while the one on the right has a spring constant, k₂= 100 N/m. A vertical and downward load, P = 40 N, is applied at a distance x from A. (i) Derive the value of x for which the beam will have a horizontal orientation at equilibrium. State and justify your assumptions and comment on your working. bewalls (ii) Assume the two springs have different unstressed lengths. In your own (exham Or words, show whether it is possible for the beam to have a horizontal orientation at equilibrium when one spring is stretched while the other spring is compressed. State and justify your assumptions and comment on your working. kı k₂ (oisse of ton) 1. etgR B 10964 mtsnimsx3 to bn3 P Figure 2.1 (not to scale) A inction, and