Unit- 2

Equilibrium

Que-1 Determine tension chord AB and BC for equilibrium of 20kg block shown in given fig

Ans- 6 F.B.D for given system

By lami’s theorem

Que-2 A circular roller of 1000N weight and 20cm radius hang by tie rod AB= 40cm and rest against a smooth vertical wall at C as shown in fig.

Determine :- the tension in rod and reaction at point C .

Ans- FBD diagram for given system

=

By lami’s theorem

Que-3 Determine the force P applied at 30 to horizontal just necessary to start a roller having 50cm radius over a 12 cm high obstruction if roller is 100 kg mass shown in fig. Below . Also find magnitude and direction of P when it is minimum.

Ans-8  F.B.D for roller

By lami’s theorem

To final p min

By lami’s theorem

For

Ques 4 Two identical rollers each of mass 50Kg are supported by an inclined plane and vertical wall as shown in Fig. Assuming smooth surfaces Find reactions induced at the point of support A,B and C

Ans   Consider FBD of both rollers and let R be the radius of rollers

Ques 5 Two spheres A and B of 1000N and 750N weight respectively are kept as shown in figure Determine reactions at all contact points P,Q,R,S

Radius of A=400mm

Radius of B=300mm

Ans Consider F.B.D. Of sphere A

By Lami’s theorem

Consider F.B.D. Of sphere B

Ques 6 Calculate support reactions for beam as shown in figure

Ans – consider F.B.D of beam AB

Que-7 Find support tractions at A and F for given fig.

Ans- consider FBD for beam DF

Consider F.B.D for beam AC

Que-8 Calculate reaction at supports A,B,C of beam loaded as shown in fig. Below by principle of virtual work

Ans  - F.B.D for given system

Lift end C about point D such that DC rotates by

By principle of virtual work

Total work done =0

Lift internal hing D such that portion AD rotates by about A and potions CD rotates by about C

Lift the entire beam AC vertically up by

Since there is no horizontal force

Que-9 Determine the reaction in overhanging beam as shown in fig. Below by vertical work method.

Ans-let us given virtual displacement at A

Displacement at AB

Displacement at centroid of udl =

=0.8

Displacement at B=0

Displacement at C      B

Rotation of moment =

Writing virtual work equation for system

Since