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Question $1$

$[12$ marks$]$

Simply supported beam with point load at any point: A $12-$meter long simply supported beam carries a point load of $15kN$ located $4$ meters from the left support. Calculate the reactions at the supports and draw the shear force and bending moment diagrams for the beam.

Question $2$

$[15$ marks$]$

Simply supported beam with UDL at any point: A $24-$meter long simply supported beam supports a uniform distributed load of $6k\frac{N}{m}$ starting $6$ meters from the left support and ending $10$ meters from the same support.

a$)$ Determine the reactions at the supports and plot the shear force and bending moment diagrams for the beam.

b$)$ Determine the moment $2$ meters from the right support

Question $3$

$[10$ marks$]$

Simply supported beam with central point load and variable end moments: A $18-$meter long simply supported beam carries a central point load of $25kN.$ The beam also has an end moment of $40kN*m$ at the left support and $30kN*m$ at the right support.

a$)$ Determine the reactions at the supports and plot the shear force and bending moment diagrams for the beam.

b$)$ Determine the moment at a distance $8$ meters from the left support

Question $4$

$[15$ marks$]$

Simply supported beam with UDL at one end: A $22-$meter long simply supported beam has a uniform distributed load of $8k\frac{N}{m}$ applied at the left end over the first $10$ meters.

a$)$ Find the reactions at the supports and draw the shear force and bending moment diagrams for the beam.

b$)$ Determine the shear force $4$ meters from the left reaction

c$)$ Determine the moment $7$ meters from the right reaction