Concept explainers
Knowing that P = Q = 150 lb, determine (a) the distance a for which the maximum absolute value of the bending moment in beam AB is as small as possible, (b) the corresponding value of |M|max. (See the hint for Prob. 7.55.)
Fig. P7.60
7.61 Solve Prob. 7.60 assuming that P = 300 lb and Q = 150 lb.
(a)
The distance a from the ends of the beam to the points where the cables should be attached if the maximum absolute value of the bending moment in the beam AB is the smallest.
Answer to Problem 7.61P
The distance a from the ends of the beam to the points where the cables should be attached if the maximum absolute value of the bending moment in the beam AB is the smallest is
Explanation of Solution
Refer Figure 1.
Write an expression to calculate the counter clockwise moment at point A.
Here,
Write an expression to calculate the counter clockwise moment at point A.
Here,
Write an expression to calculate the counter clockwise moment at point A.
Here,
Conclusion:
Refer Figure 1:
Calculate the moment about point A.
Here,
Rearrange the equation to calculate the D.
Substitute
Refer Figure 2.
Calculate the moment about point C.
Rearrange the equation to calculate the
Substitute
Refer Figure 2.
Calculate the moment about point D.
Rearrange the equation to calculate the
Substitute
The magnitude of the maximum moment is equal to the magnitude of the minimum moment.
Substitute (I) and (II) in above equation to find a.
Rearrange the equation to find a.
Thus, the distance a from the ends of the beam to the points where the cables should be attached if the maximum absolute value of the bending moment in the beam AB is the smallest is
(b)
The value of
Answer to Problem 7.61P
The value of
Explanation of Solution
Refer Figure 4.
The magnitude of the maximum moment is equal to the magnitude of the minimum moment.
Conclusion:
Substitute
Thus, the value of
Want to see more full solutions like this?
Chapter 7 Solutions
VECTOR MECH....F/ENGNRS-STATICS -CONNECT
- No. 4arrow_forward7.74 For the beam shown, draw the shear and bending-moment dia- grams, and determine the maximum absolute value of the bending moment knowing that (a) P = 7 kips, (b) P = 10 kips. 2 kips/ft 3 kips B A 8 ft + 6 ft → 6 ft → Fig. P7.74arrow_forwardA cable AB of span L and a simple beam A'B' of the same span are subjected to identical vertical loadings as shown. Show that the magnitude of the bending moment at a point C' in the beam is equal to the product T0h, where T0 is the magnitude of the horizontal component of the tension force in the cable and h is the vertical distance between point C and the chord joining the points of support A and B.arrow_forward
- 250 mm PROBLEM 4.3 18 mm The wide-flange beam shown is made of a high-strength, low alloy steel for which o, = 450 MPa. Using a factor of safety of 3.0, determine the largest couple that can be applied to the beam when it is bent about C 360 mm M. + 10 mm the z axis. [Ans. 243.3 kNm] 18 mm Fig. P4.3 and P4.4 PROBLEM 4.4 Solve Prob, 4.3. assuming thatarrow_forward7.C4 Determine the equations for the shear and bending moment curves for beams 1 and 2 shown assuming that wo = 15 kN/m and L = 3 m. Plot the shear and bending moment diagrams for each beam. TTX w = wy sin L w = wo В A L Beam 1 Beam 2 Fig. P7.C4arrow_forwardor the beam and loading shown (a)use discontinnuity functions to write the expression for w(x). include the beam reactions in this expression. (B) intergrate w(x) twice to determine v(x) and m(x). (C) Use v(x) and m(x) to plot the shear- force and bending- moment diagrams.arrow_forward
- 5.82 The simply supported wood beam, fabricated by gluing together fourwooden boards, carries the three concentrated forces. The working bending and shear stresses for the wood are 1000 psi and 600 psi, respectively. Determine the largest allowable value of the force P.arrow_forwardProblem 4.4 pleasearrow_forwardGraph the shear and bending momentarrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY