A column ABC is supported at ends A and C and compressed by an axial load P (figure (a)). Lateral support is provided at point B but only in the plane of the figure; lateral support perpendicular to the plane of the figure is provided only at A and C. The column is constructed of two channel sections (C 6 x 8.2) back to back (see figure (b)). The modulus of elasticity of the column is E = 29,100 ksi and the proportional limit is 50 ksi. The height of the column is L = 13 ft. P L 3 B 2L X X 3 Section X-X A (a) (b) P=D=D== =====

A column ABC is supported at ends A and C and compressed by an axial load P (figure (a)). Lateral support is provided at point B but only in the plane of the figure; lateral support perpendicular to the plane of the figure is provided only at A and C. The column is constructed of two channel sections (C 6 x 8.2) back to back (see figure (b)). The modulus of elasticity of the column is E = 29,100 ksi and the proportional limit is 50 ksi. The height of the column is L = 13 ft. P L 3 B 2L X X 3 Section X-X A (a) (b) P=D=D== =====

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

The structure shown in the figure consistsof a horizontal rigid bar ABCD supported by twosteel wires: one of length L and the other of length3L/4. Both wires have cross-sectional area A and aremade of elastoplastic material with yield stress sYand modulus of elasticity E. A vertical load P acts atend D of the bar.(a) Determine the yield load PY and the correspondingyield displacement dY at point D.(b) Determine the plastic load PP and the correspondingdisplacement dY at point D when theload just reaches the value PP.(c) Draw a load-displacement diagram with theload P as ordinate and the displacement dD ofpoint D as abscissa.
2.2-14 The three-bar truss ABC shown in the figure part a has a span L = 3 m and is constructed of steel pipes having a cross-sectional area A = 3900 mm² and modulus of elasticity E = 200 GPa. Identical
A solid steel bar of diameter d, = 45.0 mm is enclosed by a steel tube of outer diameter d, = 52.5 mm and inner diameter d., = 50.0 mm (see figure). Tube A В Bar End plate -d3→ Both bar and tube are 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 = 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 t, and 1, (in MPa) in the bar and tube, respectively. (Enter the magnitudes.) T, = MPа T, = MPа (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 column, pinned at top and bottom, is made up of two C 10 x 25 steel shapes (see figure) that act together. Gap- 26 ft. Note that distance d is measured between the centroids of the two C sha ve this problem using the assumptions of ideal, Assume that E = 30,000 ksi and L slender, prismatic, and linearly elastic columns (Euler buckling).) (a) Find the buckling load (in kips) if the gap is zero. 37.3 kips (b) Find required separation distance d (in inches) so that the buckling load is the same in y and z directions. 6.92 in.
2.2-4 A steel cable with a nominal diameter of 25 mm (see Table 2-1) is used in a construction yard to lift a bridge section weighing 38 kN, as shown in the figure. The cable has an effective modulus of elastic- ity E = 140 GPa. (a) If the cable is 14 m long, how much will it stretch when the load is picked up? (b) If the cable is rated for a maximum load of 70 kN, what is the factor of safety with respect to failure of the cable? ▬▬
A solid steel bar of diameter di = 1.4 in. is enclosed by a steel tube of outer diameter d3 = 2.25 in. and inner diameter d2 = 1.9 in. (see the figure). Both bar and tube are held rigidly by a support at end A and joined securely to a rigid plate at end B. The composite bar, which has length L = 26 in., is twisted by a torque T = 5,100 lb-in. acting on the end plate. Tube A Bar End plate (a) Determine the maximum shear stresses T1 and T2 in the bar and tube, respectively. Round your answers to the nearest whole number. T1 = psi T2 = psi (b) Determine the angle of rotation (in degrees) of the end plate, assuming that the shear modulus of the steel is G = 11.5 × 10° psi. Round your answer to three decimal places. (c) Determine the torsional stiffness kT of the composite bar. Round your answer to the nearest whole. [Hint: Use equations below to find the torques in the bar and tube.] T = T GIp, + G2IP, kT = k-in.
A rigid bar ACE is supported by three vertical wires and is initially horizontal, as shown in the figure. Then, a force P is applied at the center of the bar. All wires are made from the same material with modulus of elasticity E = 200 GPa and have the same cross-sectional area, A = 10 mm². You may assume that the deformations are small and that the stresses are within the elastic range for this problem. 1.5 m A D F 1.0 m 1.0 m H C E P A 2.0 m Figure 3.1: Rigid bar supported by three vertical wires a) Find the normal stresses and the axial displacements in the wires if P = 15 kN. b) Knowing that AB is the critical wire, and its yield stress is oy maximum P that can be applied. = 1500 MPa, find the
A "rigid" beam AD is supported by a smooth pin B and by vertical rods that are attached to the beam at points A and C, as shown in the Figure. Neglect the weight of the beam. The beam is horizontal when only rod (1) is attached and P= 22 kN, but rod (2) was manufacutred d' = 0.35 mm too short. Assume that rod (2) is stretched and attached to the beam at C then the load P = 22 kN is applied. [A1= 256 mm², A2= 160 mm² E₁-E₂= 200 GPa, a= 0.8 m, b= 2.5 m, L₁= 79 cm, L₂= 128 cm, 5'= 0.35 mm] L; (1) B a (2) Cl L2 15 b What is the value of the internal force in rod (1)? D
A flat bar of rectangular cross section, length L, and constant thickness tis subjected to tension by forces P (see figure). The width of the barvaries linearly from b1 at the smaller end to b2 at the larger end. Assumethat the angle of taper is small.(a) Derive the following formula Tor the elongation of the ban(b) Calculate the elongation, assuming L=5 ft, t=1.0 in., P= 25 kips, ft, =4.0 in., ft, = 6.0 bland E= 30 x 106 psi.
An AB copper bar is positioned at room temperature with a gap S of 0.0002m between the A end and a rigid constraint (see figure). The bar is supported at the B end by an elastic spring with elastic constant k= 210x10^6 N/m. Calculate the compressive stress on the bar if the temperature only on the bar increases by 27°C. (For copper, use σ = 17.5x10^-6/°C and E = 110 GPa). Despise the action of gravity
An L-shaped bracket lying in a horizontal plane supports a load P =1501b (see figure). The bracket has a hollow rectangular cross section with thickness t =0,125 in. and outer dimensions b = 2,0 in. and Ji = 3,5 in. The centerline lengths of the arms are fy = 20 in, and b:z=30 in. Considering only the load P, calculate the ma.xjmum tensile stress ut,maximum compressive stresserCJ and maximum shear stressTmaK at point A,which is located on the top of the bracket at the support,
A wooden beam (1) is reinforced with steel plates (2) rigidly attached to its top and bottom surfaces, as shown in the figure. Dimensions of the cross section are b₁ = 5.50 in., d,= 10.75 in., b₂ = 3.50 in., and d₂ = 0.55 in. The elastic moduli of the wood and steel are E₁ = 1, 250 ksi and E₂ = 30, 000 ksi, respectively. The allowable bending stresses of the wood and steel are 1200 psi and 19500 psi, respectively. Determine the largest concentrated vertical load that can be applied at midspan if a simply supported beam with this cross section spans 16.8 ft. by Jd₂ (1) 2- (2) P = (2) b₂ d₁ Td₂ eTextbook and Media: lb