- shorteningQuestion 4The inverted T beam shown in Figure Q4 carries a uniformly distributed load of 40 kN/m and a concentratedload of 75 kN.(a) Draw the bending moment diagram for the beam indicating the values at all principal sections.[13 marks](b) Calculate the second moment of area of the cross-section with respect to the horizontal neutral axis.[4 marks](c) Calculate the maximum normal stress in tension and compression due to bending.(d) Sketch the normal stress distribution over the cross-section, at the location of maximum bendingmoment, stating all important values.[4 marks][4 marks]228A40 kN/mIse1.5 mBCentroid of area of cross-section3 m75 kN- 60C2 m600V160-400Cross-section (dimensions in mm)Figure Q4tens-veCamp

(a) Drawing the bending moment diagram:The bending moment diagram shows how the bending moment…

Answered: - shortening Question 4 The inverted T…

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.5.1P: A beam with a channel section is subjected to a bending moment M having its vector at an angle 0 to...

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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.
A fixed-end beam AB of a length L supports a uniform load of intensity q (see figure). Beginning with the second-order differential equation of the deflection curve (the bending-moment equation), obtain the reactions, shear forces, bending moments, slopes, and deflections of the beam. Construct the shear-force and bending-moment diagrams, Labeling all critical ordinales.
A simple beam AB is loaded as shown in the figure. Calculate the required section modulus S if ^aibw = IS,000 psi, L = 32 ft, P = 2900 lb, and g = 450 lb/ft. Then select a suitable I-beam (S shape) from Table F-2(a), Appendix F, and recalculate 5 taking into account the weight of the beam. Select a new beam size if necessary. What is the maximum load P that can be applied to your final beam selection in part (a)?
A singly symmetric beam with a T-section (see figure) has cross-sectional dimensions b = 140 mm, a = 190, 8 mm, b. = 6,99 mm, and fc = 11,2 mm. Calculate the plastic modulus Z and the shape factor.
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 q1
A simply supported beam (L = 4.5 m) must support mechanical equipment represented as a distributed load with intensity q = 30 kN/m acting over the middle segment of the beam (see figure). Select the most economical W-shape steel beam from Table F-l(b) to support the loads. Consider both the distributed force q and the weight of the beam. Use an allowable bending stress of 140 MPa.
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 seesaw weighing 3 lb/ft of length is occupied by two children, each weighing 90 lb (see figure). The center of gravity of each child is 8 ft from the fulcrum. The board is 19 ft long, 8 in. wide, and 1.5 in. thick. What is the maximum bending stress in the board?
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.
A beam ABCD with a vertical arm CE is supported as a simple beam at .1 and D (see figure). A cable passes over a small pulley that is attached to the arm at E. One end of the cable is attached to the beam at point B. The tensile force in the cable is 1800 lb. Draw the shear-Force and bending-moment diagrams for beam A BCD. Note: Disregard the widths of the beam and vertical arm and use centerline dimensions when making calculations. Repeat part (a) if a roller support is added at C and a shear release is inserted just left of C (see figure part b).
Beam ABC is fixed at support A and rests (at point B) upon the midpoint of beam DE (see part a of the figure). Thus, beam, ABC may be represented as a propped cantilever beam with an overhang BC and a linearly elastic support of stiffness k at point B (see part b of the figure). The distance from A to B is L = 10 ft, the distance from B to C is L/2 = 5 ft, and the length of beam DE is L = 10 ft. Both beams have the same flexural rigidity EI. A concentrated load P = 1700 lb acts at t lie free end of beam ABC. Determine the reactions RA, RB+ and MAfor beam ABC. Also, draw the shear-force and bending-moment diagrams for beam ABC, labeling all critical ordinates.
Find support reactions at A and D and then calculate the axial force N. shear force 1 and bending moment 11 at mid-span of column BD. Let L = 4 m, q0 = 160N/m, P = 200N, and M0= 380 N .m.

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