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SUBJECT

WELDING & METALWORK

GRADE

DATE

APRIL 2020 WK 3

TOPIC

FORCES: MEMORANDUM

TERM 1

REVISION

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TERM 2 CONTENT

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QUESTION 1

QUESTION 2

A diagram below shows a uniform beam. The beam is supported at points RL and RR. Three point loads of 4 N, 5 N and 3 N are exerted onto the beam.

a) Calculate the reactions at supports RL and RR.

b) Calculate the bending moments at point B, C and D.

c) Draw a bending-moment diagram of the beam.

Solution a)

Reactions at the supports RL and RR:

RL x 12 = (3 x 3) + (5 x 6) + (4 x 9)

: RL = 6.25N

RR x 12 = (4 x 3) + (5 x 6) + (3 x 9)

RR = 5.75N

Solution b)

Bending moments:

BMB = (6.25 N x 3 m)

= (18.75 N.m)

BMc = (6.25 x 6) – (4 x 3)

= 25.5 N.m

BMD = (6.25 x 9) – (4 x 6) – (5 x 3)

= 17.25 N.m

Solution c)

Question 3

Solution a)

Reactions at the supports RL and RR

Moments about RR

RL x 12 = (5 x 9) + (6 x 6) + (4 x 3)

RL x 12 = 45 + 36 + 12

RL =

RL = 7,75 N

Reactions about RL

RR x 12 = (4 x 9) + (6 x 6) + (5 x 3)

RR x 12 = 36 + 36 + 15

RR =

RR = 7,25 kN

Solution b)

Shear forces:

𝑆𝐹𝐴 = 0 kN.

𝑆𝐹𝐵 = 7,75 – 5

= 2,75 kN

𝑆𝐹𝐶 = 7,75 – 5 – 6

= - 3, 25 kN

𝑆𝐹𝐷 = 7,75 – 5 – 6 – 4

= - 7,25 kN

𝑆𝐹𝐸 = 7,75 – 5 – 6 – 4 + 7,75

= 0 kN

Solution c)

Bending moments:

Solution d)

Shear force diagram:

Solution e)

Bending moment diagram:

QUESTION 4