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A 5.1 m long simply supported wood beam carries a uniformly distributed load of 11.3 kN/m, as shown in Figure A. The cross-sectional dimensions of the beam as shown in Figure B are b = 205 mm, d = 460 mm, yH = 77 mm, and yx = 162 mm. Section a-a is located at x = 1.3 m from B. (a) At section a-a, determine the magnitude of the shear stress in the beam at point H. (b) At section a-a, determine the magnitude of the shear stress in the beam at point K. (c) If the allowable shear stress for the wood is 850 kPa, what is the largest distributed load w that can be supported by the beam? х В L Figure A

2. In the figure below, a lug wrench is subjected to loads as shown. The tool body is a hollow cylinder with an outer diameter D = 25 mm, and thickness t. Ignore the changes in diameter (i.e., assume they are all the same), and model it as a cantilever beam. 250N x Z y 500N(+z) 350 mm 500 mm 350 mm 250N B 500N(-z) Cross-section A Z B Useful Cross-section properties for thin walled tubes: I = J = "D³t_A = πDt πD³t 8 a. Sketch elements A and B and show the stress states. Clearly label the coordinate axes on the elements. Make sure you calculate the normal (o) and shear stresses (T). Neglect Tv. b. Find the principal stresses for each element using Mohr's Circle.

Figure Q2 shows the cross section of a beam. The beam is simply supported over a span of 6 m and carries a vertical point load of 40 kN acting at its mid-span. Calculate  The position of the horizontal centroidal axis of the cross-section from its bottom. The second moment area of the cross-section about the horizontal centroidal axis  The maximum shear load per unit length (metre) at the lower surface of the top flange

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Determine the axial force, shear force, and bending moment at point J located on member AB of the landing gear of an airplane, as shown in the figure.All distances are in inches.

The bending moment in a horizontally placed beam at distance x from one of the ends is given by the expression M = 13x - 3x - 12 . The shear force in the beam is zero at, O a. x = 7.12 O b.x = 3 and x = 1.33 O C. X = 2.16 O d. Need more data and a figure to solve the problem.

In the following figure, there are two equal couples with a magnitude of M = 15 kNm. They act in opposite directions while being applied to the channel beam AB. These couples cause the beam to bend in the horizontal plane. Find: 1) Stress at point C 2) Stress at point D 3) Stress at point E

A cable is enacting a force, F, on a built-in hook at an angle 9 as shown in the figure. Determine the displacement of the point at which the force acts, in the direction of the cable if the shaft of the hook has a length L, radius r and elastic modulus E. Ignore the deformation of the circular hook. If E= 200 GPa, F = 50 kN, 0 = 25°, L = 1 m, r- 100 mm: Answer: 8 = 0.196 mm

Consider the two bars of identical material with their elastic modulus E as shown in Figure below. Both bars have the same circular cross-section with diameter of d. The length of the longer bar is 2L and the length of the shorter bar is L. The angle between the bars is B. The system is subjected to a vertical force acting at point Pas shown in the figure with a magnitude of F. Calculate horizontal and vertical components of the displacement of point P. Use engineering notation (ENG display mode on scientific calculators) with 3 significant figures after the decimal point. E (psi) 1.50E+06 d (in) 1.25 L (in) 12 Beta (degrees) 30 F (Ibf) 110 F P L 2L