SHEAR FORCE AND BENDING MOMENT DIAGRAM

Q.A beam of length 9 m is simply supported on a span of 5 m with an over hang of 4 m in the right hand portion. It carries a udl of 3 kN/m on a length of 5 m from LHS and a point load of 4 kN at 9 m from LHS. Draw SF and BM diagrams and state the position of point of contra flexure.

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SOLUTION: Total load 3 * 5 + 4 = 19 kN To find reactions Taking moments about A R{B} * 5 = 4 * 9 + (3 * 5) * 5/2 = 73.5 R{B} = 73.5/5 = 14.7kN RA =Total load – R{B} = 19 – 14.7 = 4.3kN SFD SHEAR FORCE DIAGRAM  F{A} = … Read more

Q. simply supported beam ABC with suports at A and B, 6 m apart with an over hang of BC = 2m long carries a udl of the whole length. Draw SFD & BMD

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SOLUTION: Total load = 20 * 8 = 160 kN To find the reactions Taking moments about A R{B} * 6 = (20 * 8) * 8/2 = 640 R{B} = 640/6 = 106.67kN R{A} = 160 – 106.67 = 53.33kN SFD (SHEAR FORCE DIAGRAM) F{A} = 53.33kN FB =just left ofB = – 66.67kN … Read more

Q. A beam of length 6 m is supported at 2 m and 6 m from the left end of the beam and carrying 10 kN and 20 kN are acting at 2 m and 6 m from the right end of the beam. Find the support reactions.

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Q. A beam of length 6 m is supported at 2 m and 6 m from the left end of the beam and carrying 10 kN and 20 kN are acting at 2 m and 6 m from the right end of the beam. Find the support reactions. SOLUTION: Total load= 20 + 10 = … Read more

Q. A horizontal beam of 12 m long simply supported at its ends, is subjected to vertical loads of 10 kN, 20 kN and 25 kN at 3 m, 7 m and 10 mm from left support respectively along with a udl of 10kN / m over a length of 3 m from left support and 6 kN/m over a length of 2 m from right support. Draw the SF and BM diagrams. Also calculate the max. B.M and its location.

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SOLUTION: Total load = 10 + 20 + 25 + 10 * 3 + 6 * 2 = 97 kN To find the reactions Taking moments about A R_{B} * 12 = 10 * 3 + 20 * 7 + 25 * 10 + (10 * 3) * 3/2 (6 * 2)(2/2 + 10) =30 … Read more

Q. A simply supported beam 6m span is carrying a udl of 4kN / m over its right half of its span and a point load of 10 kN at mid span. Draw SF and BM diagrams and find value of maximum hending moment.

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SOLUTION: Total load= 10 + 4 * 3 = 22kN To find the reactions Taking moments about A R{B} * 6 =10 * 3 + (4 * 3) (3/2+3) = 84 R_{B} = 84/6 = 14kN R{A} = 22 – 14 = 8kN SFD SHEAR FORCE DIAGRAM  F{A} = 8kN (same in AC) Fc (just … Read more

Q. A simply supported beam AB of span 6m long carries a udl of 10 kN/m over a length of 2 m from the right support. In addition to that it carries two point loads of 12 kN and 15 kN at a distances of 2 m and 3 m respectively from left support. Draw SF and BM diagrams and indicating values at salient points.

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SOLUTION: Total load = 12 + 15 + (10 * 2) = 47kN To find the reactions Taking moments about B R{A} * 6 = (10 * 2) * 2/2 + 15 * 3 + 12 * 4 = 20 + 45 + 48 = 113 R{A} = 113/6 = 18.83kN R{B} = 47 – … Read more

Q. A simply supported beam of span 6 m carries udl of 10kN / m upto a distance of 2 m from left support and a point load of 15 kN is placed at a distance of 2 m from right support. Draw the SFD and BMD and indicate where max shear force and max B.M occurs.

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SOLUTION: Total load = 10 * 2 + 15 = 35 kN To find reactions Taking moment about A R_{B} * 6 = 15 * 4 + (10 * 2) * 2/2 = 80kN R_{B} = 80/6 = 13.33kN R_{A} = 35 – 13.33 = 21.67kN SFD (SHEAR FORCE DIAGRAM) F_{A} = 21.67kN F_{B} = … Read more

Q. A simply supported beam of span 12 m carries a udl of 5kN / m over a length of 6 m on middle portion of the beam. In addition to that it carries two point loads of 20 kN and 15 kN at 1.5 m and 10 m from left hand support. Draw the SF and BM diagrams and indicate their max values.

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SOLUTION: Total load = 20 + 15 + 5 * 6 = 65kN To find the reactions Taking moments about A R{B} * 12 = 20 * 1.5 + 15 * 10 + (5 * 6)(6/2 + 3) = 360 R{B} = 360/12 = 30kN R{A} = 65 – 30 = 35kN SFD ( SHEAR … Read more

Q. A simply supported beam of span 6 m. A udl of 2 kN/m is acting on the right half of the span. A point load of 10 kN is at 2 m from the LHS. Draw SFD and BMD.

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SOLUTION: Total load = 10 + 2 * 3 = 16 kN To find reactions Taking moments about B R{A} * 6 = 10 * 4 + (2 * 3) * 3/2 = 49 R{A} = 49/6 = 8.17kN R{B} = 16 – 8.17 = 7.83kN SFD( SHEAR FORCE DIAGRAM) F{A} = 8.17kN F{B} = … Read more

Q. simply supported beam of span 6 m carrying concentrated loads of 30KN, 20 kN, 30 kN and 20 kN at distances of 1 m, 2 m, 3m and 4 m from L.H.S. Find the supported reactions.

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Q. simply supported beam of span 6 m carrying concentrated loads of 30KN, 20 kN, 30 kN and 20 kN at distances of 1 m, 2 m, 3m and 4 m from L.H.S. Find the supported reactions. SOLUTION: To find reactions : Total load = 30 + 20 + 30 + 20 = 100 kN … Read more