BE Construction Engineering Semester 1 (FE First Year) - University of Mumbai Important Questions

A force of magnitude of 20kN, acts at point A(3,4,5)m and has its line of action passing through B(5,-3,4)m. Calculate the moment of this force about a line passing through points S(2,-5,3) m and T(-3,4,6)m.

Determine the position of the centroid of the plane lamina. Shaded portion is removed.

Find the centroid of the shaded portion of the plate shown in the figure.

For the composite lamina shown in the figure, determine the coordinates of its centroid.

Determine the reaction at points of constant 1,2 and 3. Assume smooth surfaces.

Given: The spheres are in equilibrium
To find: Reactions at points 1,2 and 3

Explain the conditions for equilibrium of forces in space.

Find the support reactions at A and B for the beam loaded as shown in the given figure.

Determine the force P required to move the block A of 5000 N weight up the inclined plane, coefficient of friction between all contact surfaces is 0.25. Neglect the weight of the wedge and the wedge angle is 15 degrees.

Given : Weight of block A = 5000 N
μ_s=0.25
Wedge angle = 15^º

To find : Force P required to move block A up the inclined plane

State Lami’s theorem.
State the necessary condition for application of Lami’s theorem.

Two spheres A and B of weight 1000N and 750N respectively are kept as shown in the figure..Determine reaction at all contact points 1,2,3 and 4. Radius of A is 400 mm and radius of B is 300 mm

Given  : Two spheres are in equilibrium
W₁=1000 N
W₂=750 N
r_A=400 mm
r_B=300 mm 
To find : Reaction forces at contact points 1,2,3 and 4

Refer to figure.If the co-efficient of friction is 0.60 for all contact surfaces and θ = 30o,what force P applied to the block B acting down and parallel to the incline will start motion and what will be the tension in the cord parallel to inclined plane attached to A.
Take WA=120 N and WB=200 N.

Two blocks A and B are resting against the wall and floor as shown in the figure.Find the minimum value of P that will hold the system in equilibrium. Take μ=0.25 at the floor,μ=0.3 at the wall and μ=0.2 between the blocks.

Given : μ=0.25 at floor
             μ=0.2 between blocks
To find : Minimum value of force P

Three blocks A,B and C of masses 3 kg,2 kg and 7 kg respectively are connected as shown.Determine the acceleration of A,B and C.Also find the tension in the string.

Given : m_A=3kg
           m_B=2 kg
           m_C=7kg 
To find: Acceleration of blocks A,B and C

Block A of weight 2000N is kept on the inclined plane at 35° .It is connected to weight B by an inextensible string passing over smooth pulley.
Determine the weight of pan B so that B just moves down.Assume μ=0.2.

Given : Weight of block A=2000N
Angle of inclined plane = 35°
μ=0.2
To find : Weight of pan B 

A rod AD of length 40 cm is suspended from point D as shown in figure. If it has a weight of 25 N and also supports a load of 40N,find the tension in the cable using the method of virtual work.Take AC=30 cm.

Given : Length of rod AD=40cm=0.4m
AC=0.3m
W=25N
Load on rod AD=40N
To find : Tension in the cable

The acceleration of the train starting from rest at any instant is given by the expression `a=8/(v^2+1)` where v is the velocity of train in m/s. Find the velocity of the train when its displacement is 20 m and its displacement when velocity is 64.8 kmph.

A boom AB is supported as shown in the figure by a cable runs from C over a small smooth pulley at D.
Compute the tension T in cable and reaction at A.Neglect the weight of the boom and size of the pulley.

The given figure shows a beam AB hinged at A and roller supported at B. The L shaped portion is welded at D to the beam AB. For the loading shown,find the support reactions.

Given : Beam AB hinged at A and roller supported at B and different forces acting on it.
To find : Support reactions

If the support reaction at A, for the beam shown in Figure 3, is zero, then find force ‘P’ and the support reaction at B. 

For the truss shown in figure 4, find: (i) zero force members, if any (Justify your answer with FBD), (ii) support reactions at C and D.