Geogebra ProjectCivil and Construction

Engineering

Tsapeti Anastasia

Experimental Study Of Bending Deformation In Central Heating

About…

This exercise is a Laboratory Exercise in Physics, focused on Civil And Construction Engineering, and becomes experimental

verification of laws relating to the elastic of solid bodies.

School of Pedagogical & Technological Education (ASPETE - Athens, Greece)

We have a rod or a beam whose length is L, the width a, and the thickness b.

Then deform to bending.

The deformation corresponding to the average displacement of the rod from the original horizontal balance called...

Deflection d

The rod is base embedded at one end there of and the force P exercised in other end.

P

d

The deflection d of the rod or beam with these geometric features given by:

P

d where P is the bending force and Y is the Young’s modulus, different for each material. (http://en.wikipedia.org/wiki/Young%27s_modulus)

⇔

1

2is the surface moment of inertia of the beam

The purpose is to verify the relationship practically and that the graph is linear form i.e. : d =k ∙X

Once we construct the column , then the graphic design representation d =f (X).

From the relation provided that the function d =f (L) is third degree i.e. the arrow deflection d is proportional to the third power of the length L of the rod.

For experimental verification needs to be the first linearization data (d, L).

The experiment…

Components of the experimental setup

1) Specific contact micrometer for measuring the deflection. 

2) A different set of prismatic bars. 

3) A support system in a horizontal position of the prism rod. 

4) A set of calibrated weights together with the system of the dependence of these horizontal prismatic bars. 

5) A measure and a caliper.

The experiment… α, b, F, Y: constant

Taking measurements

Use rod dimensions: length L =50 cm, width a =20 mm, thickness b =1.5 mm. To insert the rod into the proper support system bars.

1) Adjust the length of the rod so that it is equal to L =160 mm.

2) Adjust the micrometer in the right free end of the rod and rotate the drum so that the spike sharply approaching the free edge rod. The red LED will light as soon as the tip comes into contact with the rod. For accurate determination of the minimum position of contact, rotate little backwards again correctly drum micrometer and observe the LED go off and lights respectively. In this position note indicating the micrometer, d0. That statement is a shift of zero the instrument (off-set).

For a specific bending force P kept constant parameters Y, a and b and measure the dependence of the deflection d of the length L of the prismatic rod.

3) To place the suspension system masses total mass m = 160 gr on the right end of the rod and the micrometer raised into contact with the rod by rotating the drum, i.e. until it turns on the LED, as you did in step 2. Post indication of micrometer L1 in the corresponding cell of Table.

4) Repeat operations 2) and 3) for the remaining lengths of rod indicated in Table.

F= a =20 mm b =1.5 mm 

a/aL (mm) λ0 (mm) λ1 (mm) λ=λ1-λ0

(mm)X=L3

(mm)1 1602 1503 1404 1305 1206 1107 1008 909 8010 70

Physics Laboratory

Data elements

The experiment…

• F =m.g

• The material we use is Wrought iron and we assume that: Y =197 (×109 N/m2 or GPa)

•

• !We need to be especially careful to make the appropriate modifications to the final result given in units of the S.I.

Let's see how the experiment becomes on Geogebra

Bibliography...

Physics for Scientists and Engineers, R. Knight, ION Publications, 2008 University Physics, Hugh D. Young, Papazisis, 1992 Physics Volume 1, Halliday - Resnick, Publications Spiritual Exercises Physics Laboratory I TEI Piraeus, ION Publications, 1990 Applied Physics, N. D. NANOUS, Macedonian Publications, 2003 Laboratory Experiments Physics, PHYWE

Thank our mentoring team

Nikos Matzakos (Mathematics)

Dimitris Kechrakos (Physics)

Kallia Kounenou (Counselling)

Especially…