No Dokumen SB/MMSB2/T2/BMCS2333/5

No Isu./Tarikh 1/2006

SOLID MECHANICS 2 DEFLECTION OF CANTILEVERS AND

BUILT-IN BEAMS

No Semakan/Tarikh 0

Jum Mukasurat 5

KOLEJ UNIVERSITI TEKNIKAL

KEBANGSAAN MALAYSIA

OBJECTIVE To understand and describe the deflection behaviors of cantilevers and built-in beams. THEORY In deflection of a cantilever experiment, we will examine the deflection of a cantilever subjected to an increasing point load. We will repeat this for three different materials to see if their deflection properties vary.

The deflection of a cantilever = 3

3WL

EI (1)

where, = Load (N) W = Distance from support to position of loading (m) L = Young’s modulus for cantilever material (N/mE 2) I = Second moment of area of the cantilever (m4) In deflection of a built-in beam experiment, we will examine the deflection of a built-in beam subjected to an increasing point load. This means we can find out the relationship between the deflection and the length of the beam. The maximum deflection occurs at the mid-span of beam

Maximum deflection = EI

wL192

3

(2)

where, = Load (N) W = the length of beam (m) L E = Young’s modulus for cantilever material (N/m2) I = Second moment of area of the cantilever (m4) APPARATUS Figure 1 shows the apparatus of Cantilevers and Built-in beams experiment. It consists of a backboard with a digital dial test indicator. The digital dial test indicator is on a sliding bracket, which allows it to traverse accurately to any position along the test beam. Two rigid clamps mount on the backboard and can hold the beam in any position. Two knife-edge supports also fasten anywhere along the beam. Scales printed on the backboard allow quick and accurate positioning of the dial test indicator, knife-edges and loads.

1/4

SB/MMSB2/T2/BMCS2333/5

Fixing holes

Fixing holes

Scale

Moveable digital dial test indicator

Clamp Moveable knife-edge

U-section channel

Scale

Knife-edge load hanger

Moveable

knife-edge

Clamp Figure 1

Figure 1 The beam apparatus

PROCEDURES The Deflection of Cantilevers and Built-in beams experiment fits into a Test Frame. Figure 2 shows the Deflection of Cantilevers and Built-in beams experiment in the Test Frame. Before setting up and using the equipment, always: 1. Visually inspect parts including electrical leads for damage or wear. 2. Check electrical connections are correct and secure. 3. Check all components are secure and fastenings are sufficiently tight. 4. Position the Test Frame safely. 5. Never apply excessive loads to any part of the equipment

Specimen beam

Digital dial test indicator on sliding bracket

Securing thumbscrews

Clamp (2 off)

Clamp mounting

holes

Moveable knife-edge

(2 off)

Hanger and masses

98mm

Figure 2 The Test Frame of Beam Apparatus

2/4

SB/MMSB2/T2/BMCS2333/5

EXPERIMENT 1 DEFLECTION OF A CANTILEVER In this experiment, we will examine the deflection of a cantilever subjected to an increasing point load. We will repeat this for three different materials to see if their deflection properties varied.

200mm

Figure 3 WFigure 3 Set-up of cantilever beam

1. Using a vernier gauge, measure the width and depth of the aluminum, brass and steel test beams. Record the values next to the results tables for each material and use them to calculate the second moment of area I .

2. Remove any clamps and knife-edges from the backboard. Set up one of the cantilevers as shown in Figure 3.

3. Slide the digital dial test indicator to the position on the beam shown in Figure 3, and lock it using the thumbnut at the rear. Slide a knife-edge hanger to the position shown.

4. Tap the frame lightly and zero the digital dial test indicator using the ‘origin’ button. 5. Apply masses to knife-edge hanger in the increments as shown in Table 1a 6. Tap the frame lightly each time you add the masses. Record the digital dial test indicator

reading for each increment of mass in Table 1a. 7. Repeat the procedure for the other two materials and record in the Table 1b and 1c

respectively. 8. Calculate the theoretical deflection for each beam and record your results in each

respective table. EXPERIMENT 2 DEFLECTION OF A BUILT-IN BEAM In this experiment, we will examine the deflection of a built-in-beam subjected to an increasing point load. We will repeat this for three different materials to see if their deflection properties vary. 1. Using a vernier gauge, measure the width and depth of the aluminum, brass and steel, test

beam. Record the values next to the result table and use them to calculate the second moment of area, I .

2. Remove any clamps from the backboard. Setting length between supports L up to maximum length of beam, set up the beam as shown in Figure 4.

3. Slide the digital dial test indicator into center of the beam and lock it using the thumbnut at

the rear. 4. Slide a knife-edge hanger to the center position of the beam length. 5. Tap the frame lightly and zero the digital dial test indicator using the ‘origin’ button. 6. Apply masses to the knife-edge hanger in the increments shown in the results table. Tap the

frame lightly each time, and record the digital dial test indicator reading for each increment of mass in Table 2a.

3/4

SB/MMSB2/T2/BMCS2333/5

400l mm=

7. Repeat the above procedures for the other two materials and record in the Table 2b and 2c respectively.

8. Calculate the theoretical deflection for each beam and record the results in each respective table.

W

L

Figure 4 : Built-in beam setup

W

Figure 4 Built-in setup with L = 600 mm

4/4