Draw the shear and moment diagrams for the loaded cantilever beam where the end

Question

Draw the shear and moment diagrams for the loaded cantilever beam where the end couple M1 is adjusted so as to produce zero moment at the fixed end of the beam. Then answer the questions.

At x = 4.3 ft, V =____lb, M =____lb-ft

At x = 9.9 ft, V =____lb, M =____ib-ft

The maximum (absolute value) shear force is ______lb

The maximum (absolute value) bending moment is_______lb-ft

Draw the shear and moment diagrams for the loaded cantilever beam where the end couple M1 is adjusted so as to produce zero moment at the fixed end of the beam. Then answer the questions. At x = 4.3 ft, V = lb, M = lb-ft At x = 9.9 ft, V = lb, M = ib-ft The maximum (absolute value) shear force is lb The maximum (absolute value) bending moment is lb-ft

Explanation / Answer

Given UDL of 160lb/ft. So net force acting will be 160*7.8/12= 104 lb and this will be acting at midpoint of 7.8' so at 3.9'.

and given that the left end is fixed. So Reaction at that will be equal to 104lb.

M=maximum moment = 104*7.8*2/12=135.2 lb-ft

now consider shear force diagram

Force at fixed end = 104lb

Force at 7.8' from fixed end = 104-104=0lb

now 4.3' lies between 3.9 and 7.8' so force at 4.3' will be +ve.

consider UDL upto 4.3' then u hav net force of 4.3/12*160=57.33lb/ft. so at 4.3' force will be 104-57.33= 46.66lb.

Moment at distance x from fixed end will be 104*x - 160*x^2 = 104*4.3/12 - 160*(4.3/12)^2 = 5.45lb-ft.

now at 9.9' there will be no shear force acting because shear force becomes zero at 7.8' only

Moment at 9.9' = 104*9.9/12 - 104*6/12 = 26lb-ft.

Maximum shear value of force occurs at fixed end i.e 104lb

maximum bending moment occurs at 15.6' ie 104*15.6/12 + 104*(15.6-3.9)/12 + M = 371.8lb-ft

Here M is taken as +ve because is causes shagging effect.

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