4.1 Assemble the global stiffness equations for the beam shown. Neglect axial deformation. Compute the displacements, reactions, and internal forces for the loading and support conditions indicated 15 kN (d)

EXAMPLE 4.2 The rigid bar BDE is supported by two links AB and CD. Link AB is made of aluminum (E = 70 GPa) and has a cross-sectional area of 500 mm²; link CD is made of steel (E = 200 GPa) and has a cross-sectional area of 600 mm?. For the 30-kN force shown, determine the deflection (a) of B, (b) of D, (c) of E. %3D 0.4 m 0.3 m 30 kN D E -0.4 m 0.2 m

PROBLEM 2: A two cell wing box, whose geometrical and material properties are given in the table below, is shown in the figure. This two cell section has been idealized such that the booms resist all the direct stresses while the walls are effective only in shear. A bending moment Mx = 2000 Nm and a shear load Sy = 15000 N in the plane of web 52 are applied at the larger cross-section. The distance between sections is 1000 m. (a) Calculate the forces in the booms and the shear (b) Calculate and DRAW the shear flow distribution (c) Determine the angle of twist if the span of the wing at this section Wall Thickness Boom (mm) 1.0 1.0 2.0 2.0 1.5 12, 56 23, 45 34 25 16 320mm Length (mm) 600 800 320 320 210 3 180mm 1,6 2,5 3,4 I 200mm 790 mm Boom Area (mm²) 300 400 400 15 II + 590 mm 11 Cell I II 6 Cell Area (mm²) 100 000 260 000 120 mm 120 mm 210 mm 320mm

The T-shaped beam shown above is supporting a concentrated load P at its free end. The beam has an allowable bending stress of ?????? = 250 MPa and an allowable shear stress of ?????? = 100 MPa. a) Determine the distance to the neutral axis (?̅), second moment of area (?), and the section modulus (?) of the cross-section.b) Draw the shear force diagram (SFD) and bending moment diagram (BMD) of the beam. On your diagrams, express the values of shear and moment in terms of the applied load P.c) Determine the maximum value of P such that bending failure will not occur.d) Determine the maximum value of P such that shear failure will not occur.e) Based on your answers to (c) and (d), what is the maximum load P that can be applied to the beam? Is this beam bending or shear governed?

If the allowable bending stress is σ = 247 MPa, find the magnitude of the maximum internal bending moment Mz that can be supported by the beam. The moment of inertia about the z axis is 402,238,667 mm4.

A truss is subjected to different force combinations as shown in the figure below. The cross-sectional area of each member is shown in the figure, and the Young's coefficient of the member is 200 GPa (1×109 N/m2):(a) Find the horizontal deformation (including direction) of point C.(b) Find the vertical deformation (including direction) of point C.(c) If the temperature of the rod AD increases uniformly by 60 degrees due to the relationship with the wall, and the temperature coefficient of the rod is known to be 12×10-6/°C, try to find the vertical deformation of point C again (including direction).

tate of Stress Caused by Combined Loadings Learning Goal: To use the superposition principle to find the state of stress on a beam under multiple loadings. The beam shown below is subjected to a horizontal force P via the rope wound around the pulley. The state of stress at point A is to be determined. 100 mm 15 mm 20 mm 200 mm 150 mm f 20 mm The dimensions are di - 2.15 m. d₂ = 0.5 m. -0.85 m d-285 mm and r= 150 mm The applied force has magnitude P=4.5 kN Part A-Support Reactions and Internal Loading C₁, C₂=₁ N=, V = ₁ M = Determine the support reactions C, and C, and the internal normal force, shear force, and moment on the cross-section containing point A. Express your answers, separated by commas, to three significant figures. ► View Available Hint(s) Submit Part B- Properties of the Cross-Section A= I= Q = Submit VAX IT VOC JA=.TA= What are the cross-sectional area, moment of inertia with respect to the neutral axis, and first moment of the area with respect to point A for the…

The cross-sectional dimensions of the beam shown in the figure are a = 4.8 in., b = 6 in., d = 4.0 in., and t = 0.33 in. The internal bending moment about the z centroidal axis is M₂ = -4.20 kip-ft. Determine (a) the maximum tension bending stress (a positive number) in the beam. (b) the maximum compression bending stress (a negative number) in the beam. (L Answers: (a) Omax T = (b) Omax C Z b y I (typ.) a psi psi d

If the beam is subjected to a bending moment of M = 5 kN # m, determine the bending stress developed at point A and sketch the result on a differential element at this point.

A beam had an isosceles triangular cross section (see figure below). The maximum flexural stress is limited to 90 MPa. Determine the magnitude of the allowable bending moment M. 150 mm Y = 30° 100 mm y