Force Method of Analysis $(17$ marks$)$

Use Force Method to compute all the support reactions for the following beam $($Figure $1)$ and draw the

bending moment diagram. Support at A settles down by $18$ mm and support at B settles down by $6$

mm $($these support settlements are in addition to the load acting on the beam$).$ Note that, differential

temperature is also acting on the member BC $($NOT in AB$)$ as shown in the figure. A and B are roller

supports and C is a pin support.

Take E $=200$ GPa, I $=120\backslash$times $106$ mm $4$ and coefficient of thermal expansion, $=105/\backslash$deg C$.$ Use principal

of virtual work to determine deflections. You can use integration table OR formulate general equation

while solving for deflections.

Mark distribution:

Primary Structure, redundant and compatibility equation $4$ marks

Deflection Calculations $9$ marks

Bending moment diagram $4$ marks

Total marks for Problem $117$ marks

Figure $1$

$30\backslash$deg C

$0\backslash$deg C

$250$ mm

C

$3$ m$3$ m $2$ m

A B

$30$ kN

$10$ kN$/$m

$1$ m