Further Mechanical Principles: Assignment on Beam Analysis and Forces

This assignment solution addresses a mechanical engineering problem focusing on beam analysis and force calculations. The assignment is divided into two main parts. The first part involves analyzing a pin-jointed frame, requiring graphical and analytical solutions to determine forces. The second part deals with the analysis of beams, including the calculation of reactions, shear forces, and bending moments at various points along the beam. Students are required to draw shear force and bending moment diagrams, and identify the point of contraflexure. Specific values for loads and dimensions are provided, enabling a comprehensive understanding of structural behavior under different loading conditions. This assignment is designed to enhance the student's understanding of fundamental engineering principles and their application in structural analysis.

Engineering
Programme : National Diploma in Engineering
Year 2
Unit : Further Mechanical Principles
Assignment 1
P1/M1
The diagram below shows a plane pin jointed frame subjected to vertical loads of L1
and L2. The frame is supported by a pin joint at the left-hand end and by rollers at the
right hand end. Using the allocated set of values from the table below, determine all the
forces and reactions in the frame.
1. For P1 solve the problem graphically.
2. For M1 solve the problem analytically.
Student L1 (kN) L2 (kN)
Me 40 16
THIS SHEET MUST BE RETURNED WITH THE COMPLETED WORK
Page 1 of 3
L1 L2
60º 60º 60º 60º
4m 4m

P2
1. A uniform horizontal beam which is simply supported at either end has the forces
shown below acting on it.
(a) Calculate the reactions of the supports at A and B.
(b) Calculate the shearing force and bending moment at 1m intervals along
the beam.
(c) Draw (on graph paper) the shear force and bending moment diagrams for
the loaded beam.
M2
1. The diagram below represents a light beam ABCD which is simply supported at the
points A and B. The beam carries a uniformly distributed load between A and D and
point loads LB and LD as shown. Use the allocated set of values from the table on
the next page to answer the following questions.
(a) Calculate the reactions at A and C.
(b) Calculate the shearing force and bending moment at 1m intervals along
the beam.
(c) Draw (on graph paper) the shear force and bending moment diagrams for
the loaded beam, clearly marking all point values and the position of the
point of contraflexure.
THIS SHEET MUST BE RETURNED WITH THE COMPLETED WORK
Page 2 of 3
UDL
LD
x1
A C
x2
LB
x3
DB
15kN 20kN
2.5m 4m
A B
2m
25kN
1.5m

Student x1(m) x2 (m) x3 (m) LB (KN) LD (KN) UDL (KN/m)
Me 3 2 4 35 10 10
THIS SHEET MUST BE RETURNED WITH THE COMPLETED WORK
Page 3 of 3