Chapter 12.5, Problem 98P

The beam is subjected to the load shown. The beam is made of material having an E = 200 GPa and I = 65.0 x 10-6 m4.  Using singularity functions, develop an expression for the bending moment M(x) asfunction of position (x) along the beam.

3. Determine the displacement and slope (i.e. 0) at the load point for the stepped beam shown in the following figure. Also determine the reaction forces and moments. Each element has E = 200 GPa. The area moment of inertia are given as I₁ = 1.25 × 105 mm4, and 2 = 4 x 104 mm. Clearly show the elemental stiffness matrices (k) for each element, assembly of k matrices to get global stiffness matrix (K) and application of boundary conditions. Then solve the reduced K matrix to get displacements and reactions 3000 N 150 mm 75 mm 125 mm

2 - Use double integration to determine the elastic curve of the cantilever beam under lateral loading, where w is the load intensity (per unit length) at the left end. Flexural rigidity is El. Show that the tip displacement is: y w w14 U(L)=-30EI

determine the diagram of the shear forces and bending moments in the beam shown below. Data P = 20kN, M = 60kNm, q = 10kN / m, a = 5m, b = 2m, c = 3, alpha = 60.

For the beam shown, determine in terms of W, L, E, and I: The equation of the elastic curve The rotations at points A and B Deflection of point C The maximum deflection of the beam Check the results of parts b and c using the Area Moment Method

A force tangent to 1.75 feet diameter pulley is 5200 N and is mounted on a 2 inches shaft. Determine the torsional deflection per meter of length if G = 83 x 106 Kpa.

The simply supported shaft has a moment of inertia of 2I for region BC and a moment of inertia I for regions AB and CD. Determine the maximum deflection of the shaft due to the load P.

The beam ABis attached to the wall in the zz plane by a fixed support at A. A force of F = (- 156i + 58.0j + 350k) N is applied to the end of the beam at B. The weight of the beam can be modeled with a uniform distributed load of intensity w = 65.0 N/m acting in the negative z direction along its entire length. Find the support reactions at Á. F B y а Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value 5.80 m 5.00 m 3.80 m A = i+ j- k) N MA = k) N-m

Part A - Free-body diagram of the resolved components of the moments   The two externally applied moments can be resolved into their respective y and z components. Determine the moments in each principal direction, My and Mz, and draw the corresponding free-body diagram.     Part B - Moments of inertia of the cross section with respect to the y- and z-axes To calculate the absolute maximum bending stress in the member using the flexure formula for unsymmetrical bending, the moments of inertia of the cross section must be calculated. Select the correct formulas for these values. Iy=?     Part C - Neutral-axis angle due to externally applied moments   The neutral-axis angle of the cross section being analyzed is the axis along which there is a zero stress value. Determine the neutral-axis angle, αα, due to the externally applied moments as measured counterclockwise from the positive z axis in the yz plane. |α| =? Part D - Absolute maximum stress in cross section ABCD…