Concept explainers
5.1 through 5.6 For the beam and loading shown, (a) draw the shear and bending-moment diagrams, (b) determine the equations of the shear and bending-moment curves.
Fig. P5.6
(a)
To draw: The shear and bending-moment diagrams.
Explanation of Solution
Determine the reactions of the beam.
Show the free-body diagram of the entire beam as in Figure 1.
Determine the vertical reaction at point D by taking moment about point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Substitute wa for
Determine the horizontal direction at point A by resolving the horizontal component of forces.
Show the free-body diagram of the section 1-1 as in Figure 2.
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Show the free-body diagram of the section 2-2 as in Figure 3.
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Show the free-body diagram of the section 3-3 as in Figure 4.
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Shear force and bending moment values:
Show the calculated shear force and bending moment values as in Table 1.
Location (x) | Shear force (V) | Bending Moment (M) |
A | wa | 0 |
B (1-1) | 0 | |
B (2-2) | 0 | |
C (2-2) | 0 | |
C (3-3) | 0 | |
D | –wa | 0 |
Plot the shear force and bending moment diagrams as in Figure 5.
(b)
The equations of the shear and bending-moment curves.
Answer to Problem 6P
The equation of shear force and bending-moment curves is:
For section AB;
For section BC;
For section CD:
Explanation of Solution
Determine the reactions of the beam.
Show the free-body diagram of the entire beam as in Figure 6.
Determine the vertical reaction at point D by taking moment about point A.
Determine the vertical reaction at point A by resolving the vertical component of forces.
Substitute wa for
Determine the horizontal direction at point A by resolving the horizontal component of forces.
Show the free-body diagram of the section 1-1 as in Figure 7.
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Show the free-body diagram of the section 2-2 as in Figure 8.
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Show the free-body diagram of the section 3-3 as in Figure 9.
Determine the shear force at the section by resolving the vertical component of forces.
Determine the moment at the section by taking moment about the section.
Therefore, the equation of shear force and bending-moment curves is:
For section AB;
For section BC;
For section CD:
Want to see more full solutions like this?
Chapter 5 Solutions
Mechanics of Materials, 7th Edition
- 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 5.16arrow_forwardProblem 5.14 please thanksarrow_forward
- 0.6 m 25 kN/m 40 kN 1.8 m 40 KN C 0.6 m D PROBLEM 5.108 (a) Using singularity functions, write the equations for the shear and bending moment for the beam and loading shown. (b) Determine the maximum value of the bending moment in the beam.arrow_forwardSection 5.1 5.1 through 5.11 Determine the axial forces, shears, and bending moments at points A and B of the structure shown. 40 k Hinge A B | | | 10 ft + 5 ft 5 ft FIG. P5.8 10 ft 40 k + 10 ftarrow_forward6.68 The manufactured wood beam carries the concentrated loads shown. What is the maximum safe value of P if the working stress in shear is 6 MPa?arrow_forward
- number threearrow_forward- -.... .. . and 5.8 beam and loading shown, and determine the maximum absolute value (a) of the shear, (b) of the bending moment. Draw the shear and bending-moment diagrams for the 200 N 200 N 500 N 200 N A C D' E 300 225 300 225 Dimensions in mm Fig. P5.8arrow_forwardProblem 5.15arrow_forward
- number fivearrow_forwardProblem 5.64 2.5 k/ft Draw the shear, bending moment, and axial force diagrams and the qualitative deflected shape for the frame shown. 12 ft 30 k 12 ft D 20 ft FIG. P5.64arrow_forwardDraw the shear and bending-moment diagrams for the beam and loading shown, and determine the maximum absolute value (a) of the shear, (b) of the 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