Task 4. Construction shear force and bending moment diagrams for beams

Construct shear force and bending moment diagrams for four beams loaded as shown in fig. 4. Assume: F = qa; l = a; M = qa ².

Take the data necessary for computation from table 5.

table 5

variant /group No./
q, kN/m
a, m	1.1	1.2	1.3	1.4	1.5	1.6	0.7	0.8	0.9	1.5

Order of work

1. Draw the design scheme for the beam; indicate all dimensions and loads using letters and digits.

2. Determine values of support reactions; show them on the computation diagram using letters and digits.

3. Determine number of the beam sections and numerate them. Mark each section beginning and end.

4. Using the method of sections write the equations for determination shear force Q and bending moment M _b for each section. Use value of boundary conditions in the equations to calculate Q and M _b.

5. Construct the diagrams Q and M _b.

For one of the beams of task 4 (by the teacher's choice) select I-beam section under condition of strength by normal stresses. Check up strength of the beam by shear stresses assume the allowable value of normal stress [ s ] = 160 MPа to computate.

1. On М _b diagram determine the greatest value of bending moment M_max for the selected beam. Under condition of bending strength determine the moment of résistance W_y .

2. Select I-beam number using the "I-beams" guide and calculated value W _y.

3. check the strength of the beam by the greatest value of normal and shear stresses.

Fig.5. (see also p.15)

Fig.5. Continued (see also p.16)

Fig.5. Continued (see also p.17)

Fig.5. Continued (see also p.18)

Fig.5. Continued (see also p.19)

Fig.5. Continued (see also p.20)

Fig.5. Ending

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