Q.2. A beam ABC with an overhang at one end supports a uniform load of intensity 12 kN/m and a concentrated load of magnitude 2.4 kN as shown in figure (2). Draw the shear-force and pending-moment diagrams for this beam. A 12 kN/m 16m- B -1.6 m- Fig (2) 2.4 kN -1.6 m- |
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- Two identical, simply supported beams AB and CD are placed so that they cross each other at their midpoints (sec figure). Before the uniform load is applied, the beams just touch each other at the crossing point. Determine the maximum bending moments (mab)max* and (MCD)max beams AB and CD, respectively, due to the uniform load if the intensity of the load is q = 6.4 kN/m and the length of each beam is L = 4 m.The beam ABC shown in the figure is simply supported at A and B and has an overhang from B to C. The loads consist of a horizontal force P1= 4,0 kN acting at the end of a vertical arm and a vertical force P2= 8.0 kN acting at the end of the overhang, Determine the shear force Fand bending moment M at a cross section located 3,0 m from the left-hand support. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations, Find the value of load A that results in V = 0 at a cross section located 2.0 m from the left-hand support. If P2= 8.0 kN, find the value of load P1that results in M = 0 at a cross section located 2,0 m from the left-hand support.At a full d raw, an archer applies a pull of 130 N to the bowstring of the bow shown in the figure. Determine the bending moment at the midpoint of the bow.
- Find expressions for shear force V and moment M at mid-span of beam AB in terms of peak load intensity q0and beam length variables a and L Let a = 5L/b.A C 200 x 17.1 channel section has an angle with equal legs attached as shown; the angle serves as a lintel beam. The combined steel section is subjected to a bending moment M having its vector directed along the z axis, as shown in the figure. The cent roi d C of the combined section is located at distances xtand ycfrom the centroid (C1) of the channel alone. Principal axes yl and yvare also shown in the figure and properties Ix1,Iy1and 0pare given. Find the orientation of the neutral axis and calculate the maximum tensile stress exand maximum compressive stress if the angle is an L 76 x 76 x 6.4 section and M = 3.5 kN - m. Use the following properties for principal axes for the combined section:/^, = 18.49 X 106 nrai4,/;| = 1.602 X 106 mm4, ep= 7.448*(CW),_r£ = 10.70 mm,andvf= 24.07 mm.A cantilever beam AB having rectangular cross sections with varying width bxand varying height hxis subjected to a uniform load of intensity q (sec figure). If the width varies linearly with x according to the equation hx= bBxiL^ how should the height hxvary as a function of v in order to have a fully stressed beam? (Express hxin terms of the height hBat the fixed end of the beam.)
- The cross section of a composite beam made of aluminum and steel is shown in the figure. The moduli of elasticity are TA= 75 GPa and Es= 200 GPa. Under the action of a bending moment that produces a maximum stress of 50 M Pa in the aluminum, what is the maximum stress xs in the steel? If the height of the beam remains at 120 mm and allowable stresses in steel and aluminum are defined as 94 M Pa and 40 M Pa, respectively, what heights h and h. arc required for aluminum and steel, respectively, so that both steel and aluminum reach their allowable stress values under the maximum moment?A beam supporting a uniform load of intensity q throughout its length rests on pistons at points A, C and B (sec figure). The cylinders are filled with oil and are connected by a tube so that the oil pressure on each piston is the same. The pistons at A and B have diameter d1and the piston at C has diameter D2. (a) Determine the ratio of d2to d1so that the largest bending moment in the beam is as small as possible. Under these optimum conditions, what is the largest bending moment Mmaxin the beam? What is the difference in elevation between point C and the end supports?Two flat beams AB and CD, lying in horizontal planes, cross at right angles and jointly support a vertical load P at their midpoints (see figure). Before the load P is applied, the beams just touch each other. Both beams are made of the same material and have the same widths. Also, the ends of both beams are simply supported. The lengths of beams AB and CD are LABand LCD, respectively. What should be the ratio tABltCDof the thicknesses of the beams if all four reactions arc to be the same?
- A wood beam reinforced by an aluminum channel section is shown in the figure. The beam has a cross section of dimensions 150 mm x 250 mm, and the channel has a uniform thickness of 6.5 mm. If the allowable stresses in the wood and aluminum are 8 M Pa and 38 M Pa, respectively, and if their moduli of elasticity are in the ratio 1 to 6, what is the maximum allowable bending moment for the beam?The beam ABC shown in the figure is simply supported at A and B and has an overhang from B to C Draw the shear-force and bending-moment diagrams for beam ABC. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations.2. For the 20 meter beam shown, there is a roller at "A" (Ay = 52 kN; it is acting upward), and a pin joint at "B" (By=-- 17 kN; it is acting downward). (a) Draw complete shear force and bending moment diagrams. (b) If x=0 is at the left end of the beam, write equations for the shear force and bending moment, and indicate the appropriate sections. (You may use the table on the next page.) 50 KN 15 KN A 90 kN-m 2 m3 m -5 m B *4 -7 m 120 kN-m € 3 m