Chapter 4.1: Shear and Moment Diagram
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2 Chapter 4.1: Shear and Moment Diagram Chapter 5: Stresses in Beams Chapter 6: Classical Methods
3 Beam Types Generally, beams are classified according to how the beam is supported and according to crosssection variance. A beam maybe determinate or indeterminate depending on the support conditions.
4 Determinacy pertains to the complexity of analysis of a particular beam with loadings. Determinate beams are beams whose support reactions may easily be determined from equations of equilibrium. Indeterminate beams are beams whose support reactions cannot all be determined from conditions of equilibrium.
5 1. Simply Supported Determinate Beams 2. Cantilever 3. Overhanging Beams
6 1. Propped Beams Indeterminate Beams 2. Restrained Beams 3. Continuous Beams
7 Beam Shear and Bending Moment Beam shear simply relates the transverse loads and reactions along the beam. Bending Moment is the moment reaction of the beam against flexure or bending. To determine the beam shear and bending moment along any part of the beam, pass a cutting plane normal to the beam.
8 Shear and Moment Equations and Diagrams Shear and Moment on beams can be determined from using equations or from diagrams the latter being the preferred option. Again, in order to determine the shear and moment for specific parts or segments of the beam, a cutting plane must be passed through beam.
9 To determine the shear at the cut section, employ summation of forces. To determine moment at the cut section, take summation of moment about the cut section itself. For the diagrams, it is important to remember that the shear diagram is higher than the load diagram by one mathematical degree. Consequently, the moment diagram is also higher than the shear diagram by one mathematical degree.
10 Beam Shear and Bending Moment However, some conventions must be established: ( + ) Positive ( - ) Negative
11 Conventions and other rules regarding the shear and moment diagram are best discussed in the proceeding examples. ( + ) Positive For Positive (+) Conventions, (1) Shear Forces that tend to bend a beam element clockwise. (2) Bending moments that tend to bend a beam element concave upward (the beam smiles ).
12 Conventions and other rules regarding the shear and moment diagram are best discussed in the proceeding examples. ( - ) Negative For Negative (-) Conventions, (1) Shear Forces that tend to bend a beam element counter clockwise. (2) Bending moments that tend to bend a beam element concave downward (the beam sad face ).
13 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 14 kn 28kN A B C D 2 m 3 m 2 m
14 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 16 kn.m A B C 3 m 1 m
15 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 20 kn A B A 15 kn/m C 2 m 4 m
16 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 20 kn/m A B 3m
17 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 10 kn/m 20 kn/m A B 3m
18 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 10 kn/m A 10 kn.m B 2m 1m
19 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. A B A 20 kn/m C D 2 m 4 m 2 m
20 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 10 kn 20 kn/m A B C D E 10kN/m 2m 1m 1m 2m
21 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 5 kn 10 kn/m 10 kn/m A B C D E F 4m 1m 1m 3m 3m
22 Example : Determine the shear and moment equations of the beam given below and draw the shear and moment diagrams. 20 kn/m 10 kn/m A B 2m 1m
23 Example : Draw the load and the bending moment diagrams that correspond to the given shear force diagram. Assume that no couples are applied to the beam. V (kn) 48 kn 28 kn 8 kn 2m 2m 2m 1m 1m X (m) -20 kn -32 kn
24 Example : Draw the load and the bending moment diagrams that correspond to the given shear force diagram. V (kn) 20 kn 10 kn 2m 1m 1m 0.5 m 1.5 m X (m) -30 kn
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1 of 6 EQUILIBRIUM OF A RIGID BODY AND ANALYSIS OF ETRUCTURAS II 9.1 reactions in supports and joints of a two-dimensional structure and statically indeterminate reactions: Statically indeterminate structures
3. BEAMS: STRAIN, STRESS, DEFLECTIONS
3. BEAMS: STRAIN, STRESS, DEFLECTIONS The beam, or flexural member, is frequently encountered in structures and machines, and its elementary stress analysis constitutes one of the more interesting facets