The figure shows a cantilever consisting of steel angles size 100 x 100 x 12 mm mounted back to back. Using superposition, find the deflection at B and the maximum stress in the beam. 3 m - 2.5 kN 2 m I kN/m B A
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- Compound beam ABC is loaded by point load P = 1.5 kips at distance 2aB from point A and a triangularly distributed load on segment BC with peak intensity qü= 0.5 kips/ft. If length a = 5 ft and length/) = 10 ft, find the deflection at B and rotation at A. Assume that £ = 29,000 ksi and / = 53.8 in4.-5 Calen1ate the deflections S 3a ndA simply supported beam (E = 1600 ksi) is loaded by a triangular distributed load from A to C(see figure). The load has a peak intensity q0= 10 lb/ ft, and the deflection is known to be 0.01 in, at point C. The length of the beam is 12 ft, and the ratio of the height to the width of the cross section is (h:b) 2:1, Find the height h; and width h of the cross section of the beam.
- A cantilever beam has a length L = 12 ft and a rectangular cross section (b = 16 in., h = 24 in.), A linearly varying distributed load with peak intensity q0acts on the beam, (a) Find peak intensity q0if the deflection at joint B is known to be 0.18 in. Assume that modulus E = 30,000 ksi. (b) Find the location and magnitude of the maximum rotation of the beam.A cantilever beam(Z, = 6 ft) with a rectangular cross section (/> = 3.5 in., h = 12 in.) supports an upward load P = 35 kips at its free end. (a) Find the state of stress ((7T, o^., and r in ksi) on a plane-stress element at L/2 that is i/ = 8 in. up from the bottom of the beam. Find the principal normal stresses and maximum shear stress. Show these stresses on sketches of properly oriented elements. (b) Repeat part (a) if an axial compressive centroidal load N = 40 kips is added at BA thin, high-strength steel rule (E = 30 x 10ft psi) having a thickness t = 0.175 in. and length L = 48 in. is bent by couples Mcinto a circular arc subtending a central angle a = 40° (sec figure), What is the maximum bending stress emax. in the rule? By what percent docs the stress increase or decrease if the central angle is increased by 10%? What percent increase or decrease in rule thickness will result in the maximum stress reaching the allowable value of 42 ksi?
- A cantileverbeam^Cßsupportstwo concentrated loads Ptand A, as shown in the figure. Calculate the deflections SBand 8Cat points B and C, respectively. Assume Px= 10 kN, P\ = 5 kN, L = 2.6 m, E = 200 GPa, and / = 20.1 x I0ft mm4.A wide-flange beam (W 12 x 35) supports a uniform load on a simple span of length L = 14 ft (see figure). Calculate the maximum deflection max at the midpoint and the angles of rotation Sat the supports if q = 1.8 kips/ft and E = 30 × 106 psi. (Use the formulas of Example 9-1.)The cantilever beam AB shown in the figure has an extension BCD attached to its free end. A force P acts at the end of the extension. Find the ratio aiL so that the vertical deflection of point B will be zero. Find the ratio aiL so that the angle of rotation at point B will be zero.
- A beam ABC with simple supports at A and B and an overhang BC supports a concentrated load P at the free end C (see figure). Determine the strain energy Ustored in the beam due to the load P. From the strain energy, find the deflection Scunder the load P. Calculate the numerical values of £/and Sc if the length L is 8 ft, the overhang length a is 3 ft, the beam is a W 10 x 12 steel wide-flange section, and the load P produces a maximum stress of 12,000 psi in the beam, (Use £ = 29 X 106 psi.)A simply supported slender column is subjected to axial load P = 175 kips applied at distance e = 0,5 in. from joint s A and B (see figure). The column has a circular cross section with an outer diameter of 10 in. and wall thickness of 0.5 in. Calculate the height of the column if the maximum deflection caused by the axial loads is 0,1 in. Assume that E = 29,000 ksi.Each girder of the lift bridge (sec figure) is 180 ft long and simply supported at the ends. The design load for each girder is a uniform load of intensity 1,6 kips/ft. The girders are fabricated by welding three steel plates to form an I-shaped cross section (see figure) having section modulus S = 3600 in3. What is the maximum bending stress rmaxin a girder due to the uniform load?