# STRENGTH OF MATERIALS

TABLE OF CONTENTS

INTRODUCTION

Deflection of beams and cantilevers is an important study for clear understanding of behavioral properties of various structural components in aircrafts and around us. Various aircraft structural components such as wing and fuselage ribs and spars (or longerons) require structural analysis for research and cross-examination.

Our aim is to study the phenomenal deflection changes experienced during beam and cantilever deflection, we will be conducting controlled experiments of various beam materials and sizes and we will also be studying change of properties such as shape deflection and circular bending.

This lab experiment report details our practical and theoretical experimentation with graphical aids and reasoning.

DESCRIPTION OF THE EXPERIMENT

We will set up the required tools and materials to experiment and study the deflection of a cantilever, simply supported beam, shape of a simply supported beam and circular bending in accordance to the instructions in the provided lecturer’s guide. REQUIRED TOOLS AND MATERIALS

Backboard with a digital dial test indicator (to measure amount of deflection) Two moveable knife-edge supports (adjustable for experimentation).

Knife-edge load hanger (To hang the masses).

Two clamps (To secure beam).

Five Hanger and masses (For adjustable weight configurations).

Aluminum, steel and brass beams (different material configurations).

Reading scale (For accurate measurement and placement).

EXPERIMENT 1 - DEFLECTION OF A CANTILEVER

VALUES FOR ALUMINUM

Material

Aluminium

E value: 69x109 Nm-2

Width (b): 19 mm

I: 4.275x10-11 m4

Depth (d): 3 mm

Mass (g)

Actual Deflection (mm)

Theoretical Deflection (mm)

0

0

0

100

-1.07

0.89

200

-2.15

1.77

300

-3.03

2.66

400

-4.04

3.54

500

-4.31

4.43

VALUES FOR STEEL

Material

Steel

E value: 207x109 Nm-2

Width (b): 19 mm

I: 4.275x10-11 m4

Depth (d): 3 mm

Mass (g)

Actual Deflection (mm)

Theoretical Deflection (mm)

0

0

0

100

-0.34

0.30

200

-0.74

0.59

300

-1.21

0.89

400

-1.53

1.18

500

-1.58

1.48

VALUES FOR BRASS

Material

Brass

E value: 105x109 Nm-2

Width (b): 19 mm

I: 4.275x10-11 m4

Depth (d): 3 mm

Mass (g)

Actual Deflection (mm)

Theoretical Deflection (mm)

0

0

0

100

-1.07

0.89

200

-2.15

1.77

300

-3.03

2.66

400

-4.04

3.54

500

-4.31

4.43

DEFLECTION VERSUS MASS FOR ALL THREE BEAMS ON SAME AXIS

(Where ) [W is load (N), L is distance (support to support), E is Young’s modulus, I is second moment of area]

RELATIONSHIP BETWEEN MASS AND DEFLECTION

The relationship is linear, as mass increases, deflection increases.

RELATIONSHIP BETWEEN GRADIENT AND MODULUS

Modulus of elasticity determines amount of deflection, the beam starts to deform after the elastic point, and the deflection becomes plastic.

TAPPING FRAME FOR ACCURACY OF DIGITAL DIAL TEST INDICATOR

Tapping the frame helps overcome any existing ‘stiction’, thus resetting the indicators detecting accuracy.

THREE PRACTICAL APPLICATIONS FOR CANTILEVER SUPPORT STRUCTURE A Balcony, a lamppost, bridge (Two beams supported at each end) and an aircraft wing structure (Cessna 182).

THEORETICAL VS PRACTICAL ACCURACY

The equation detects the theoretical deflection quite close to the practical deflection values, however since the force or the load is assumed positive the sign convention is positive for theoretical values, resulting in a inverted graph.

EXPERIMENT 2 - DEFLECTION OF A SIMPLY SUPPORTED BEAM

Material

Aluminium

E value: 69x109 Nm-2

Width b: 19 mm

I: 4.275x10-11 m4

Depth d: 3 mm

Mass (g)

Actual Deflection (mm)

Theoretical Deflection (mm)

0

0

0.00

100

-0.46

0.44

200

-0.95

0.89

300

-1.47

1.33

400

-1.84

1.77

500

-1.93

2.21

(Where ) [W is load (N), L is distance (support to...

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