Christchurch Polytechnic Institute of Technology CPIT SCHOOL OF ENGINEERING 1 Superposition Beam Deflection.docx Copyright CPIT 2010 Page 1 S Tomsett Date 22 May 2014 Superposition Beam Deflection “The total deflection of a beam can be found by adding the deflections resulting from each load acting alone on the beam.” Example Part 1: Calculate the end deflection for the cantilever shown if EI = 345 Nm 2 [15.53 mm] Part 2: Calculate the deflection at 300 mm from the wall. [2.48 mm] Part 3: Calculate the load on a simple support placed under the free end. [16 N] Problem 1 Calculate the deflection at the following distances from the wall: 300, 500, 700, 800 mm. [5.14 mm; 12.44 mm; 20.93 mm; 25.43 mm] Problem 2 a) Calculate the deflection under the 5 N load. [4.151 mm] b) Calculate the deflection at the end of the beam. [6.076 mm] c) Calculate the load on a prop placed under the 5 N load to obtain a zero deflection at the END of the beam. [9.938 N] d) What is the deflection at the 5 N load with the prop in place? [0.1 mm] 300 mm 700 mm 50 N 10 N 500 mm 300 mm 900 N 600 N EI = 6.83 x 10 3 Nm 2 500 mm 250 mm 10 N 5 N 250 mm EI = 345 Nm 2
Christchurch Polytechnic Institute of Technology CPIT SCHOOL OF
ENGINEERING
1 Superposition Beam Deflection.docx Copyright CPIT 2010 Page 1
S Tomsett Date 22 May 2014
Superposition Beam Deflection The total deflection of a beam can
be found by adding the
deflections resulting from each load acting alone on the
beam.
Example Part 1: Calculate the end deflection for the cantilever
shown if EI = 345 Nm2 [15.53 mm]
Part 2: Calculate the deflection at 300 mm from the wall. [2.48
mm] Part 3: Calculate the load on a simple support placed under the
free end. [16 N] Problem 1 Calculate the deflection at the
following distances from the wall: 300, 500, 700, 800 mm. [5.14 mm;
12.44 mm; 20.93 mm; 25.43 mm]
Problem 2
a) Calculate the deflection under the 5 N load. [4.151 mm] b)
Calculate the deflection at the end of the beam. [6.076 mm] c)
Calculate the load on a prop placed under the 5 N load to obtain a
zero deflection at the
END of the beam. [9.938 N] d) What is the deflection at the 5 N
load with the prop in place? [0.1 mm]
300 mm 700 mm
50 N 10 N
500 mm 300 mm
900 N 600 N
EI = 6.83 x 103 Nm2
500 mm 250 mm
10 N 5 N
250 mm
EI = 345 Nm2
Christchurch Polytechnic Institute of Technology CPIT SCHOOL OF
ENGINEERING
1 Superposition Beam Deflection.docx Copyright CPIT 2010 Page 2
S Tomsett Date 22 May 2014
Problem 3 Two simply supported beams are joined at their centres
and load of 100 kN is applied. Calculate the force taken by each
beam and the deflection at the load. (Hint Deflections are equal at
the centre and the total force is spread between the two beams)
[33.3 and 66.6 kN, 55.55 mm]
Problem 4 Two cantilevers and pinned together and support a 50
kN load at the pin. Both beams have E = 200 GPa, I = 12 x 10-6 m4
and are 150 mm deep. Determine the load in each beam, the
deflection at the pin and the stress in each beam. [38.6 kN 11.4
kN, 2.74 mm, 85.7 MPa 192.8 MPa] If the beam with the highest
stress was made stronger (larger I value) what would happen the
stress in that beam? [Would go up]
Problem 5 Determine the stress in the wire. [ 88.5 MPa]
