Q1/ A beam (ABC) is supported at A&B and carries a uniformly distributed loads between AB of 60N/m and downward load of magnitude 40 N at C. Find (RA) & (RB). Take AB= 6m & BC=1m ?
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- Find expressions for shear force V and moment M at v = L/2 of beam AB in structure (a). Express V and M in terms of peak load intensity q0and beam length variable L. Repeat for structure (b) but find Fand M at m id-span of member BC.Cantilever beam AB carries an upward uniform load of intensity q1from x = 0 to L/2 (see Fig. a) and a downward uniform load of intensity q from x = L/2 to L. Find q1in terms of q if the resulting moment at A is zero. Draw V and M diagrams for the case of both q and qtas applied loadings. Repeat part (a) for the case of an upward triangularly distributed load with peak intensity q0(see Fig. b). For part (b), find q0, instead of q1At 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.
- A fixed-end beam AB of a length L is subjected to a uniform load of intensity q acting over the middle region of the beam (sec figure). Obtain a formula for the fixed-end moments MAand MBin terms of the load q, the length L, and the length h of the loaded part of the beam. Plot a graph of the fixed-end moment MAversus the length b of the loaded part of the beam. For convenience, plot the graph in the following nondimensional form: MAqL2/l2versusbL with the ratio b/L varying between its extreme values of 0 and 1. (c) For the special case in which ù = h = L/3, draw the shear-force and bending-moment diagrams for the beam, labeling all critical ordinates.A beam made up all woun equal leg angles is subjected to a bending moment M having its vector .u an angle (i) lo lire axis (see figure paria). (a) For the position shown in lire figure, determine lire orienlalion of lire neulral axis and calculate lire maximum tensile s'av-s ir, and maximum compressive stress (b) The two angles are now inverted and attached back-lo-back lo lorn, a lintel beam that supports two courses of brick facade i see figure part b). Find the new orientation of the neutral axis and calculate the maximum tensile slress r. a::d maximum compressive s'avsrr . in I he beam using 6 = 30° and M = 30 kip-in.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.
- 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 fixed-end beam AB supports a uniform load of intensity q = 75 lb/ft acting over part of the span. Assume that EI = 300kip-ft2. Calculate the reactions at A and B. Find the maximum displacement and its location. Repeat part (a) if the distributed load is applied from A to B.A simply supported beam ABC is loaded at the end of a bracket BDE (see figure). Draw axial-force, shear-force, and bending-moment diagrams for ABC.
- Find the extern al re actions at support A (fix-end) for the beam shown in the figure. 7 kN 4 kN/m 30 kN m A B -2 m 3 m 5 m 2 m 3 m-Problem 3: A bent beam ABCD is held in equilibrium by a roller at A and by a pinned connection at D. The beam supports a uniform distributed load (80 lb/ft) over section AB and a concentrated force (390 lb) at point C. The roller at A rests against an inclined surface that is oriented 30° from the horizontal direction. Neglect the weight and depth of the beam and the size of the roller in this analysis. (a) Draw a complete FBD of beam ABCD. Clearly label all loads, reactions, and distances. (b) Determine all reactions at A and D. 80 lb/ft 30°/ 8 ft B 4 ft D 390 lb 12/12 3 ftQ3- A beam ABCD is simply supported at B and C with AB = CD= 2 m ; BC = 4 m. It carries a point load of 60 kN at the free end A, a uniformly distributed load of 60 kN/m between B and C and an anticlockwise moment of 80 kN m the plane of the beam applied at the free end D. Sketch and dimension the S.F. and B.M. diagrams and determine the position and magnitude of the maximum bending moment.