A rigid beam ABC is pin connected to the ground at A. A cable BD is pin-connected to the beam at B and pin-connected to the ground at D (see figure (a) below). The cross-section area of BD is 200 mm². Two forces with a magnitude of P are applied on the beam at C and E. The cable BD is made of steel and has the bilinear stress-strain behavior shown in figure (b). The slope between 0- 400 MPa is 200 GPa. The slope for stresses larger than 400 MPa is 20 GPa. Note that Hooke's law is only valid for stresses below 400 MPa. a) What is the elongation of the cable BD when P = 5 kN? b) If a vertical displacement at B is 25 mm due to forces P, what is the magnitude of P? c) In part b), if all loads are released, what is the residual vertical displacement of point C? Note: you can assume that strains are small enough that changes of geometry due to the deformation can be neglected when performing statics calculations and that the small angle approximation can be used to analyze deformations due to the rotation of the rigid beam. MPa 3 m D A 2m JP E 4 m B 2 m C 400 E = 200 GPa (a) Rigid beam with cable and (b) stress-strain curve. E' = 20 GPa E (b)

A rigid beam ABC is pin connected to the ground at A. A cable BD is pin-connected to the beam at B and pin-connected to the ground at D (see figure (a) below). The cross-section area of BD is 200 mm². Two forces with a magnitude of P are applied on the beam at C and E. The cable BD is made of steel and has the bilinear stress-strain behavior shown in figure (b). The slope between 0- 400 MPa is 200 GPa. The slope for stresses larger than 400 MPa is 20 GPa. Note that Hooke's law is only valid for stresses below 400 MPa. a) What is the elongation of the cable BD when P = 5 kN? b) If a vertical displacement at B is 25 mm due to forces P, what is the magnitude of P? c) In part b), if all loads are released, what is the residual vertical displacement of point C? Note: you can assume that strains are small enough that changes of geometry due to the deformation can be neglected when performing statics calculations and that the small angle approximation can be used to analyze deformations due to the rotation of the rigid beam. MPa 3 m D A 2m JP E 4 m B 2 m C 400 E = 200 GPa (a) Rigid beam with cable and (b) stress-strain curve. E' = 20 GPa E (b)

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

See similar textbooks

Similar questions

A solid steel bar of diameter d, = 45.0 mm is enclosed by a steel tube of outer diameter dz = 52.5 mm and inner diameter d, = 50.0 mm (see figure). Tube Bar End plate -dz Both bar and tube are held rigidly by a support end A and joined securely to a rigid plate at end B. The composite bar, which has a length L = 380 mm, is twisted by a torque T= 350 N-m acting on the end plate. (Assume that the +x-axis begins at A and extends to the right.) (a) Determine the maximum shear stresses r, and r, (in MPa) in the bar and tube, respectively. (Enter the magnitudes.) MPa 72 MPa (b) Determine the angle of rotation o (in degrees) of the end plate, assuming that the shear modulus of the steel is G = 80 GPa. (Use the statics sign convention.) (c) Determine the torsional stiffness k- (in kN · m/rad) of the composite bar. kN - m/rad
A rigid bar AB of a length L = 66 in. is hingedto a support at A and supported by two vertical wiresattached at points C and D (see figure). Both wires havethe same cross-sectional area (A = 0.0272 in2 ) and aremade of the same material (modulus E = 30 x106psi).The wire at C has a length h =18 in. and the wire at Dhas a length twice that amount. The horizontal distancesare c = 20 in. and d = 50 in.(a) Determine the tensile stresses σC and σD in thewires due to the load P = 340 lb acting at end Bof the bar.(b) Find the downward displacement δB at end B ofthe bar.
Three prismatic bars, two of material A andone of material B, transmit a tensile load P (see figure).The two outer bars (material A) are identical. Thecross-sectional area of the middle bar (material B)is 50% larger than the cross-sectional area of oneof the outer bars. Also, the modulus of elasticity ofmaterial A is twice that of material B.(a) What fraction of the load P is transmitted bythe middle bar?(b) What is the ratio of the stress in the middle barto the stress in the outer bars?(c) What is the ratio of the strain in the middle barto the strain in the outer bars?
*2.2-12 The horizontal rigid beam ABCD is supported by vertical bars BE and CF and is loaded by vertical forces P = 400 kN and P2 = 360 kN acting at points A and D, respectively (see figure). Bars BE and CF are made of steel (E = 200 GPa) and have cross-sectional areas ABE = 11,100 mm² and AcF = 9,280 mm². The distances between various points on the bars are shown in the figure. Determine the vertical displacements 84 and dp of points A and D, respectively. 1.5 m - 1.5 m – 2.1 m A B D P = 400 kN 2.4 m P2 = 360 kN 0.6 m E
A steel wire (E = 200 GPa) of diameter d = 1.0 mm is bent around a pulley of radius R0 = 400 mm (see figure below).a. What is the maximum stress in the wire?b. Does the stress increase or decrease if the radius of the pulley is increased?
2.3-8 A rectangular bar of length L has a slot in the middle half of its length (see figure). The bar has width b, thickness t, and modulus of elasticity E. The slot has width bl4. (a) Obtain a formula for the elongation & of the bar due to the axial loads P. (b) Calculate the elongátion of the bar if the mate- rial is high-strength steel, the axial stress in the middle region is 160 MPa, the length is 750 mm, and the modulus of elasticity is 210 GPa. (c) If the total elongation of the bar is limited to 8max = 0.475 mm, what is the maximum length of the slotted region? Assume that the axial stress in the middle region remains at 160 MPa. b L L 2 4
The rigid element ABCD is supported by a pin at C and two rods at A and D as shown in the figure. A load P is applied at B.[L₁ = 600 mm, A₁ = 67 mm², E₁ = 200 GPa, L₂ = 180 mm, A₂ = 647 mm², E₂ = 100 GPa, a = 600 mm, b = 350 mm, c = 300 mm, and P = 64 kN] T a. Determine the axial force and normal stress in in rod 1 and rod 2 b. Determine the displacement at point A and D
As in the figure, two cylindrical rods, one steel and the other brass, are combined in C. In A and E, the rods are flush-mounted. A) Find the reaction forces in A and E for the loading in the figure. (Esteel = 200 GPa and Rice = 105 GPa) Find (a) the reaction forces at A and E, (b) the displacement at point C.
Three identical circular disks A, B, and C arewelded to the ends of three identical solid circular bars(see figure). The bars lie in a common plane and thedisks lie in planes perpendicular to the axes of the bars.The bars are welded at their intersection D to form arigid connection. Each bar has diameter d1 = 0.5 in.and each disk has diameter d2 = 3.0 in.Forces P1, P2, and P3 act on disks A, B, and C,respectively, thus subjecting the bars to torsion. IfP1 = 28 lb, what is the maximum shear stress τmax inany of the three bars?
A solid steel bar of diameter d1= 25.0 mm is enclosed by a steel tube of outer diameter d3= 37.5 mm and inner diameter d2= 30.0 mm (see figure). Both bar and tube arc held rigidly by a support at end A and joined securely to a rigid plate at end B. The composite bar, which has a length L = 550 mm, is twisted by a torque T = 400 N ·m acting on the end plate.
An element is composed of a circular steel tube, which is enclosed by a steel cylinder as shown in the figure. The element is subjected to a compressive force P=20 KN. The aluminum cylinder has an outside diameter of 10 mm and a modulus of elasticity Ea=75 GPa. The steel tube has an outer diameter of 3 mm and a modulus of elasticity Eac = 190GPa. The element has a length L = 200 mm. Determine: compressive stresses in aluminum cylinder and steel tube. the compressive forces in the aluminum cylinder and the steel tube. The contraction of the element product of the force P.
A rigid bar of weight W = 750 lb hangs fromthree equally spaced wires: two of steel and one ofaluminum (see figure). The diameter of the wires is1/8 in. Before they were loaded, all three wires hadthe same length.What temperature increase ΔT in all threewires will result in the entire load being carriedby the steel wires? (Assume ES = 30 x106 psi,αS =6.5x10-6 /°F , αa =12x10-6 /°F