3. Determine the displacement and slope (i.e. 0) at the load point for the stepped beamshown in the following figure. Also determine the reaction forces and moments. Eachelement has E = 200 GPa. The area moment of inertia are given as I₁ = 1.25 × 105mm4, and 2 = 4 x 104 mm. Clearly show the elemental stiffness matrices (k) foreach element, assembly of k matrices to get global stiffness matrix (K) and application ofboundary conditions. Then solve the reduced K matrix to get displacements and reactions3000 N150 mm75 mm125 mm

Answered: 3. Determine the displacement and slope…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter10: Statically Indeterminate Beams

Section: Chapter Questions

Problem 10.3.6P: A cantilever beam of a length L and loaded by a uniform load of intensity q has a fixed support at A...

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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.
Beam ACE hangs from two springs, as shown in the figure. The springs have stiffnesses kxand k2and the beam has flex lira I rigidity EL (a) What is the downward displacement of point C, which is at the midpoint of the beam, when the moment M0 is applied? Data for the structure are as follows: M0= 10,0 kN m, L = 1.8 m, EI = 216 kN m2, Jt, = 250 kN/m, and k2= 160 kN/m, (b) Repeat part (a), but remove A/() and apply a uniform load q — 3.5 kN/m to the entire beam.
A temporary wood flume serving as a channel for irrigation water is shown in the figure. The vertical boards forming the sides of the flume are sunk in the ground, which provides a fixed support. The top of the flume is held by tic rods that are tightened so that there is no deflection of the boards at that point. Thus, the vertical boards may be modeled as a beam AB, supported and loaded as shown in the last part of the figure. Assuming that the thickness t of the boards is 1,5 in., the depth d of the water is 40 in., and the height h to the tie rods is 50 in., what is the maximum bending stress in the boards? Hint: The numerically largest bending moment occurs at the fixed support.
A beam A BCD rests on simple supports at B and C (see figure). The beam has a slight initial curvature so that end A is 18 mm above the elevation of the supports and end D is 12 mm above. What moments Mtand M^, acting at points A and Dtrespectively, will move points A and D downward to the level of the supports? (The flexural rigidity EI of the beam is 2.5 X 106 N m2 and L = 2.5m).
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.
The cantilever beam ACE shown in the figure has FlexuraI rigidity EI = 2,1 x 106kip-in". Calculate the downward deflections Scand 8Sat points C and B, respectively, due to the simultaneous action of the moment of 35 kip-in. applied at point C and the concentrated load of 2,5 kips applied at the free end B.
Beam ABC is loaded by a uniform load q and point load P at joint C. Using the method of superposition, calculate the deflection at joint C. Assume that L = 4 m, a =2ra, q = 15 kN/m, P = 7.5 kN, £ = 200 GPa, and / = 70.8 X 106 mm4.
The Z-section of Example D-7 is subjected to M = 5 kN · m, as shown. Determine the orientation of the neutral axis and calculate the maximum tensile stress c1and maximum compressive stress ocin the beam. Use the following numerical data: height; = 200 mm, width ft = 90 mm, constant thickness a = 15 mm, and B = 19.2e. Use = 32.6 × 106 mm4 and I2= 2.4 × 10e mm4 from Example D-7
The cantilever beam ACB shown in the figure has moments of inertia /, and I{in parts AC and CB, respectively. Using the method of superposition, determine the deflection 8Bat the free end due to the load P. Determine the ratio r of the deflection 8Bto the deflection S:at the free end of a prismatic cantilever with moment of inertia /] carrying the same load. Plot a graph of the deflection ratio r versus the ratio 12 //L of the moments of inertia. (Let /, II- vary from I to 5.)
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?
A sign of weight W is supported at its base by four bolls anchored in a concrete footing. Wind pressure P acts normal to the surface of the sign; the resultant of the uniform wind pressure is force fat the center of pressure (C.P). The wind force is assumed to create equal shear forces F/4 in the y direction at each boll (see figure parts a and c). The overturning effect of the wind force also causes an uplift force R at bolts A and C and a downward force (— R) al bolts B and D (see figure part b). The resulting effects of the wind and the associated ultimate stresses for each stress condition are normal stress in each boll (h — 60 ksi); shear through the base plate (th = 17 ksi); horizontal shear and bearing on each bolt ( tfur = 25 ksi and cr^ = 75 ksi): and bearing on the bottom washer at B (or D) (abor = 50 ksi).
-4-4 A cantilever beam is supported at B by cable BC. The beam carries a uniform load q = 200 N/M. If the length of the beam is L = 3 m, find the force in the cable and the reactions at A. Ignore the axial flexibility of the cable.

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