shearforce and bending moment space diagram ......space diagram scale – 1 : 20 30n 20n rl= rr =...

SHEARFORCE AND BENDING MOMENT

BEAMS : A beam is a structural member designed to support variousloadings applied at points along the member.

TYPES OF LOADINGS

1.Concentrated loads 2. Uniformly distributed loads

3. Varying distributed loads 4. Concentrated/distributed loads

SHEARFORCE AND BENDING MOMENT

Shearforce (vertical shear ): The shearforce at any cross-section of thebeam is equal to the algebraic sum of the external forces acting on oneside of the section only.Unit of shearforce is the same as force, i.e Newton (N).

Space Diagram Scale 1: 20

20N 30N 10N

A B C D

1m 2m 2m 2m

ERL RR

Load line scale10mm = 10N

+ PDZERO SHEAR

-

BM max

maxdist

BENDING MOMENT CALCULATION

BM scale = Space diagram scale (SDS) x Loadline scale (LLS) x Polar distance (PD)

BM max = Scale x Distance(Unit = Nm or KNm)

LINK OR FUNICULAR POLYGON

SHEAR FORCE DIAGRAM POLAR DIAGRAM

BENDING MOMENT DIAGRAM

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SPACE DIAGRAM SCALE 1:20

12kN 4kN 6KN

RL = RR =

LOAD LINESCALE: 10mm = 4 kN

+ O

(i) Find the magnitude of the reactionsRL and RR.

(ii) Find the point of application of theresultant force.

(iii) Construct the shear force diagram.(iv) Draw the bending moment

diagram.(v) Find the maximum bending

moment.(vi) What is the magnitude of the

force?

SHEET NO: 1

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Space Diagram scale – 1 : 20

60N

RL= RR =

The diagram shows a beam which carries loads at certain distance.

(a) Find the reactions RL and RR.(b) Draw the shear force and bending moment diagram.(c) Find the magnitude and the position of the equilibrant force(d) Find the maximum bending moment.

LOAD LINE SCALESCALE: 10mm =10N

+ O

BEAMSSHEET NO: 2

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Space Diagram scale – 1 : 20

30N 20N

RL= RR =

The diagram shows a beam which carries loads at certain distance.

(a) Find the reactions RL and RR.(b) Draw the shear force and bending moment diagram.(c) Find the magnitude and the position of the equilibrant force(d) Find the maximum bending moment.

LOAD LINE SCALESCALE: 10mm =10N

+ O

BEAMSSHEET NO: 3

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Space Diagram scale – 1 : 20

30N 20N 40N

RL= RR =

The diagram shows a beam which carries loads at certain distance.

(a) Find the reactions RL and RR.(b) Draw the shear force and bending moment diagram.(c) Find the magnitude and the position of the equilibrant force(d) Find the maximum bending moment.

LOAD LINE SCALESCALE: 10mm =20N

+ O

SHEEET NO: 40BEAMS

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GIVEN: The space diagram of a beam supported at the ends withpoint loads to a scale of 1: 20.

40 KN 50 KN 60 KN

RL = RR =

REQUIRED: i) Label the spaces using Bow’s Notation. (1 mark)ii) Determine the reactions RL and RR. (4 marks)iii) Draw the line of equilibrant force. (1 mark)iv) What is the magnitude of the resultant

force? (1 mark)v) Obtain the bending moment scale and

find the maximum bending moment. (4 marks)

Maximum BM =

vi) Draw the shear force diagram ( 2 marks)vii)Draw the bending moment diagram. (2 marks)

LOAD LINESCALE: 10mm = 20KN

POLE O

SHEET NO: 4

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Space Diagram scale – 1 : 20

50N 40N 10N 25 N

RL= RR =

The diagram shows a beam which carries loads at certain distance.

(a) Find the reactions RL and RR.(b) Draw the shear force and bending moment diagram.(c) Find the magnitude and the position of the equilibrant force(d) Find the maximum bending moment.(e) Draw a suitable beam design which can carry the loads given.

LOAD LINE SCALESCALE: 10mm =20N

+ O

SHEET NO: 5

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SPACE DIAGRAM SCALE 1:20

12kN 4kN 6kN

RL = RR =

LOAD LINESCALE: 10mm = 4 kN

+ O

(i) Find the magnitude of the reactionsRL and RR.

(ii) Find the point of application of theresultant force.

(iii) Construct the shear force diagram.(iv) Draw the bending moment

diagram.(v) Find the maximum bending

moment.(vi) What is the magnitude of the

force.

BEAMS

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SPACE DIAGRAM SCALE 1:2020N 30N 25N

RL = RR =

LOAD LINESCALE 10mm = 20N

+ O

1. Label the spaces using BowsNotation.

2. Determine the magnitude of thereactions RL and RR.

3. Draw the shear force diagram.4. Determine the bending moment

at 20N and at 30N force.5. Draw the line of equilibrant

force.

BEAMS

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SPACE DIAGRAM SCALE 1:20

2KN 5KN 7KN 2KN

RL = RR =

LOAD LINESCALE 10mm = 2KN

+ O

1. Use Bows Notation to label the spaces.2. Determine the magnitude of the reaction

at each support.3. Draw the line of action of the resultant

force.4. Draw the shear force diagram.5. Find the maximum bending moment.

BEAMS

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