Soil Mechanics II 2 – Basics of Mechanics 1. Definitions 2. Analysis of stress and strain in 2D – Mohr's circle 3. Basic mechanical behaviour 4.
Chapter 2 Mechanics of Materials F
F Tensile stress (+)
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Force N / m2 Normal stress =
Fluid Mechanics 2 (ME253) Dr. Gasser E. Hassan Fall 2011
Lecturer Gasser Hassan
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ENGINEERING SCHOOL OF MECHANICAL AND MANUFACTURING ENGINEERING
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Hydraulics and Pneumatics
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EDEXCEL HIGHERS ENGINEERING THERMODYNAMICS H2 NQF LEVEL 4 TUTORIAL No. 1 – PRE-REQUISITE STUDIES FLUID PROPERTIES
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QE Topics List: Structural Mechanics August 2003
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Spring 2007 – Introduction to Fluid Mechanics Homework # 2 – Chapter 1
EdExcel Mechanics 2 Statics of rigid bodies Chapter Assessment 1. Overhead cables for a tramway are supported by uniform, rigid, horizontal beams of weight 1500 N and length 5 m. Each beam, AB, is freely pivoted at one end A and supports two cables which may be modelled by vertical loads, each of 1000 N, one m from A and the other at 1 m from B. The beam is supported by a light wire, attached at one end to the beam at B and at the other to the point C which is 3 m vertically above A, as shown in the diagram below. C wire 3m m A
beam 1000 N
Calculate the tension in the wire.
(ii) Find the magnitude and direction of the force on the beam at A.
2. A uniform ladder of length 8 m and weight 180 N rests against a smooth, vertical wall and stands on a rough, horizontal surface. A woman of weight 720 N stands on the ladder so that her weight acts at a distance x m from its lower end, as shown in the diagram.
20° 8m 720 N
The system is in equilibrium with the ladder at 20° to the vertical. (i)
Show that the frictional force between the ladder and the horizontal surface is F N, where F 90(1 x) tan 20 . 
EdExcel Mechanics 2 (ii) Deduce that F increases as x increases and hence find the values of the coefficient of friction between the ladder and the surface for which the woman can stand anywhere on the ladder without it slipping.
3. A simple lift bridge is modelled as a uniform rod AD of length m and weight 5000 N. The rod is freely hinged at B and rests on a small support at C; AB = m and BC = m, as shown in the diagram below. The bridge closed is represented by the rod being horizontal. A (i)
Calculate the forces acting on the bridge due to the hinge at B and support at C. 
A lump of concrete of mass M kg is placed at A to ‘counterbalance’ the bridge to make it easier to open. For the bridge to stay firmly closed, the force at C must be 25 N vertically upwards. (ii) Calculate the value of M.
With the lump of concrete attached, the bridge is held open at 60° to the horizontal by means of a light rope of negligible mass attached to D. The rope pulls upwards at an angle of 10° to the horizontal, as shown in the diagram below. rope 10°
A (iii) Calculate the tension in the rope.
4. A uniform beam AB of length 3 m and weight 80 N is freely hinged at A. Initially, the beam is held horizontally in equilibrium by a small, smooth peg at C
Taking moments about B: 720 sin 20(8 x ) 180 sin 20 4 R sin 20 8 F cos 20 8 0
720(8 x ) 720 7200 sin 20 8F cos 20 0 F 900 90 90(8 x ) tan 20 F 90( 9 8 x )tan 20 F 90(1 x )tan 20 (ii) Since all terms in the expression for x are constant except for x, and x is positive, then as x increases F must increase. If the woman stands at the top of the ladder, x = 8. The maximum frictional force required 90 9 tan 20 810 tan 20 F R
F 810 tan 20 R 900
Since all other forces are vertical, the force at the hinge must be vertical.