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Cork Institute of Technology Bachelor of Engineering (Honours) in Structural Engineering - Stage 1

(Bachelor of Engineering in Structural Engineering – Stage 1) (NFQ Level 8)

Summer 2005

**Engineering Mechanics
**

(Time: 3 Hours)

Instructions:
Attempt **five** questions
This paper contains **seven** questions
**All** questions carry equal marks
Take g = 9.81 m/s2

Examiners: Mr. T. Corcoran Prof. P. O’ Donoghue Mr. B. O’ Rourke

Q. 1 The hinged plate shown in Figure Q. 1 has a uniform mass of 15kg and measures

0.7m x 0.45m. The tension in the supporting cable AB is 143.4 N. Determine the

moment due to this tension force about the origin, O.

Orthogonal x, y, z axes are in accordance with the right-hand rule, with origin, O as

indicated in the figure.

Q.2 The plane pin-jointed framework shown in Figure Q. 2 is supported by a pin at A and

a roller at D. The framework is subjected to a combination of vertical and horizontal

loads applied at the joints as indicated. Determine the support reactions. Use the

*method of joints* to calculate the forces in the members.

Indicate on a neat sketch of the framework the magnitude (kN) and type (tensile or

compressive) of each member force.

Q. 3 The beam shown in Figure Q. 3 is supported by a pin at A and a roller at C. The beam

is subject to a uniformly distributed load of 12 kN/m vertically along its full length

along with two additional vertical point loads of 12 kN and 9 kN as indicated in the

figure. Determine the reactions at A and C. Draw the shear force and bending moment

diagrams for the beam noting all significant values.

Q. 4 Fresh water in a channel is contained by a uniform 2.5m plate as shown in

Figure Q. 4. The plate is hinged at point A. Determine the weight of the gate (as

newtons per metre length of horizontal length into the paper) in order that it will open

when the water level reaches 0.9 m.

The density of fresh water may be taken as 1000 kg/m3.

Q. 5 A 4.0 m high square concrete column of cross-section 400mm x 400mm is reinforced

axially with 6 no. 20 mm diameter high tensile steel reinforcing bars. The applied load

acting axially on the column is 2500 kN in addition to its self-weight. Determine the

stresses in the concrete and the steel for the total load acting on the column. Determine

also the amount by which the column will shorten under this total load. You may

disregard the weight of the steel reinforcement.

Young’s modulus for concrete = 27 kN/mm2

Young’s modulus for steel = 205 kN/mm2

Unit weight of concrete = 24 kN/m3

Q. 6 A rock is allowed to fall from the edge of a cliff that is 122.5m high. Determine (a) its

velocity after 3 seconds, (b) the distance it will have travelled after 3 seconds, (c) the

length of time it takes for the rock to reach the base of the cliff, and (d) its velocity on

reaching the base of the cliff.

Q. 7 A pile driver with a mass of 1000 kg is set to fall freely through a distance of 5.0m

before striking a precast concrete pile of mass 500 kg. When the pile is almost fully

driven, the average resistance is 700 kN. Determine a) the striking velocity of the pile

driver, b) the common velocity of the pile driver and pile immediately after impact, c)

the penetration per blow at that stage and, d) the loss of kinetic energy at impact.