The overhang beam is subjected to the uniform distributed load having an intensity of w=60 kN/m. (Figure 1) Figure -3 m B W 50 mm 3 m 100 mm 1 of 1 > Part A Determine the maximum shear stress developed in the beam. Express your answer to three significant figures and include the appropriate units. Tmax= Provide Feedback μA Value Units ?
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- -6 Calculate the maximum deflection of a uniformly loaded simple beam if the span length L = 2.0 m, the intensity of the uniform load q = 2.0 kN/m, and the maximum bending stress = 60 MPa, The cross section of the beam is square, and the material is aluminum having modulus of elasticity E = 70 GPa. (Use the formulas of Example 9-1.)The compound beam shown in the figure consists of a cantilever beam AB (length L) that is pin-connected to a simple beam BD (length 2L). After the beam is constructed, a clearance c exists between the beam and a support at C, midway between points B and ZX Subsequently, a uniform load is placed along the entire length of the beam. What intensity q of the load is needed to close the gap at C and bring the beam into contact with the support?A gold-alloy microbeam attached to a silicon wafer behaves like a cantilever beam subjected to a uniform load (see figure). The beam has a length L = 27.5 m and rectangular cross section of a width b = 4.0 m and thickness t = 0.88 m. The total load on the beam is 17.2 N. If the deflection at the end of the beam is 2.46 m is what is the modulus of elasticity Egof the gold alloy? (Use the formulas of Example 9-2.)
- A thin-walled aluminum tube of rectangular cross section (sec fig me) has a centerline dimensions b = 6.0 in. and b = 4.0 in. The wall thickness t is constant and equal to 0.25 in. Determine the shear stress in the tube due to a torque T = 15 kip-in. Determine the angle of twist (in degrees) if the length L of the tube is 50 in. and the shear modulus G is 4.0 x 106 psi.Derive the following formula for the distance e from the centerline of the wall to the shear center S for the hat section of constant thickness shown in the figure: Also, check the formula for the special case of a channel section (a = 0).Beam AB has an elastic support kR at A, pin support at B, length L, height h (see figure), and is heated in such a manner that the temperature difference T2T1 between the bottom and top of the beam is proportional to the distance from support A. Assume the temperature difference varies linearly along the beam: T2T1=T0x in which T0 is a constant having units of temperature (degrees) per unit distance. Assume the spring at A is unaffected by the temperature change. Determine the maximum deflection max of the beam, Repeat for a quadratic temperature variation along the beam, so T2T1=T0x2 What is max for parts (a) and (b) if kR goes to infinity?
- A cantilever beam model is often used to represent micro-clectrical-mechanical systems (MEMS) (sec figure}. The cantilever beam is made of polysilicon (E = 150 GPa) and is subjected to an electrostatic moment M applied at the end of the cantilever beam. 1 f dimensions arc h — 2 [im, h — 4 ^m, and L = 520 ^mt find expressions for the tip deflection and rotation of the cantilever beam in terms of moment M.A cable CD of a length H is attached to the third point of a simple beam AB of a length L (see figure). The moment of inertia of the beam is I, and the effective cross-sectional area of the cable is A. The cable is initially taut but without any initial tension, (a) Obtain a formula for the tensile force S in the cable when the temperature drops uniformly by T degrees, assuming that the beam and cable are made of the same material (modulus of elasticity E and coefficient of thermal expansion . Use the method of superposition in the solution, (b) Repeat part (a), assuming a wood beam and steel cable.A cantilever beam of length L = 2 m supports a load P = 8,0 kN (sec figure). The beam is made of wood with cross-sectional dimensions 120 mm x 200 mm. Calculate the shear stresses due to the load/"at points located 25 mm, 50 mm, 75 mm, and 100 mm from the top surface of the beam. From these results, plot a graph showing the distribution of shear stresses from top to bottom of the beam.
- A uniformly tapered lube AB of circular cross section and length L is shown in the figure. The average diameters at the ends are dAand d£= 2d t. Assume E is constant. Find the elongation S of the tube when it is subjected to loads P acting at the ends. Use the following numerical data:^ = 35 mm, L = WO mm, E = 2.1 GPa. and P = 25 tN. Consider the following cases. (a) A hole of constant diameter dAis drilled from B toward A to form a hollow section of length x - U2. (b) A hole of variable diameter a\.x) is drilled, from B toward A to form a hollow section of length x = L/2 and constant thickness t = dA/20.A simple beam AB of length L and height /; undergoes a temperature change such that the bottom of the beam is at temperature 7™, and the top of the beam is at temperature Tx(see figure). Determine the equation of the deflection curve of the beam, the angle of rotation 9Aat the left-hand support, and the deflection 8mjLXat the midpoint.A cantilever beam of a length L = 2.5 ft has a rectangular cross section {b = 4in,, h = Sin,) and modulus E = 10,000 ksi. The beam is subjected to a linearly varying distributed load with a peak intensity qQ= 900 lb/ft. Use the method of superposition and Cases 1 and 9 in Table H-l to calculate the deflection and rotation at B.