Tutorial 1 FORCE SYSTEM

Transcription

1 Tutorial 1 FORCE SYSTEM 1 Find out the magnitude and direction of the resultant with reference to horizontal axis for the system shown in fig. The forces F1,F and F3 all of which act on a point A of the bracket shown in fig. are specified in three different ways. Determine the x and y component of each of the three forces. 3 Determine the resultant of the force system shown in fig. 4 A point A is pulled by pull P and is held in equilibrium by rigid cables AB and AC as shown in fig.. find magnitude and direction of force P, if both cable should carry equal tension of 500N 5 Two cables are tied together at C and loaded as shown in fig.. Determine the tension in AC and BC.

2 6 Two shafts A of 300 KN and B of 500 KN are supported as shown in fig. Neglecting friction at the contact surfaces P, Q, R and S, determine the reactions at R and S on shaft A.

3 1 A force of 800 N acts on a bracket as shown. Determine the moment of the force about B. Refer fig Tutorial CO PLANNER NON CONCURRENT FORCES Find out the moments of forces given in fig about O. Each square grid is of 1cm x 1cm. 3 Find the moment of the forces about points A and B for the system shown in fig. 4 Replace the force system of fig by a single force and a couple acting at the origin.

4 5 Determine the resultant of the system of parallel forces as shown in the fig 6 A thin rectangular plate shown in fig. is subjected to three forces. Determine the magnitude and direction of the resultant force and locate the point on the edge EDC through which the resultant is passing.

5 Tutorial 3 SUPPORT REACTION Find the Support reaction for the beams shown below 1 3 4

6 Tutorial 4 CENTER OF GRAVITY AND MOMENT OF INERTIA 1 Find the centroid and Moment of Inertia of the area of the section shown in fig.

7 Tutorial 5 SHEAR FORCE AND BENDING MOMENT DIAGRAM Draw Shear force and Bending Moment Diagram for the Beam shown below kN 00kN 160kN A 40kN/m B m m m m m 4 30kN 5kN B 5kN /m 6kN /m 1.5m m 1.5m 1.5m.5m (c)

8 Tutorial 6 SIMPLE STRESS AND STRAIN 1 A steel bar, 0 mm in diameter and m long is subjected to an axial pull of 35 kn. If E = 00 GPa, calculate the elongation of the bar. An M.S. bar 30 cm long is divided into three sections AB, BC and CD, each section being 10 cm long. The cross sectional area of the bar is 4 cm and it is loaded as shown below. Determine the total elongation of the bar if E = 00 kn/mm A B C D 50000N Aluminium 0000N 0000N 50000N 10 cm 10 cm 10 cm 3 In the bar shown as below, determine the force P so that the bar ABCD is in equilibrium. Also determine the change in length of the car. Assume E = 00 kn/mm. 100kN A 100cm 50cm 40cm 00kN P 1 B 500mm 000mm 4000mm 4 A 500 mm long bar has rectangular cross-section 0 mm x 40 mm. this bar is subjected to i) 40 kn tensile force on 0mm x 40mm face ii) 00 kn compressive force on 0mm x 500 mm faces, and iii) 300 kn tensile force on 40mm x 500mm faces. Find the change in volume if E = x 10 5 N/ mm and = A reinforced concrete column of 40 cm diameter supports a load of 500 kn axially. The reinforcement consists of 8 steel roads each of cm in diameter. Find how much load is carried by the rods and the concrete if Young s modulus of steel us 15 times that of concrete. C 3 D 150kN

9 Tutorial 7 PRINCIPAL STRESS AND STRAIN 1 An element in a strained body is subjected to two mutually perpendicular tensile stress of 300 N/mm and 00N/mm determine on a plane inclined at 30º to the direction of smaller stress: i. normal stress ii. Shear stress iii. Resultant stress [Ans.: 300N/mm, 43.3 N/mm, N/mm ] A point in a strained material is subjected to a tensile stress of 100N/mm and a compressive stress of 80 N/mm acting on two mutually perpendicular planes and a shear stress of 0 N/mm acts along these planes. Determine the following stresses on a plane inclined at 40º with the plane compressive stress : i. normal stress ii. Shear stress iii. Resultant stress [Ans 45.36N/mm, 85.16N/mm, 96.47N/mm ] 3 A strained element is subjected to stress shown in the figure determine : i. Normal and shearing stress at an angle 30º with X-axis ii. Principal stress with direction iii. Maximum shearing stress with inclination of planes. ` [Ans.: 1.96N/mm, 116.6N/mm, -96.6N/mm ] D 60 N/mm 80 N/mm E A 60 N/mm 10 N/mm 10 N/mm 60 N/mm C 60 N/mm 80 N/mm C