No Dokumen: SB/MMSB2/T2/BMCS2333/2

No Isu./Tarikh 1/2006

SOLID MECHANICS 2 CURVED BARS AND DAVITS TEST

No Semakan/Tarikh 0

Jum Mukasurat 4

KOLEJ UNIVERSITI TEKNIKAL KEBANGSAAN MALAYSIA

OBJECTIVE To find the relationship between the applied load, horizontal and vertical deflections of the four test structures; quarter circle, semicircle, curved davit and angled davit structures. THEORY Energy method is a method of determining the stresses and deformations in structures subjected to both static and impact loading. For example, a beam such as shown in Figure 1 that subjected to transverse loads, the strain energy associated with the normal stress is

2

0 2L MU dx

EI= ∫ (1)

where, M = bending moment EI = flexural rigidity of the beam = beam length L

Figure 1 A simply supported beam

A B

Lx

Load, P

Castigliano’s theorem states that the deflection jx , of the point of application of a load jP

measured along the line of action of jP is equal to the partial derivative of the strain

energy of the structure with the respect to the load jP . It can be show as

jj

UxP∂

=∂

(2)

Hence, the theorem can be applied to determine deflections and slopes at various points of a given structure. The use of “dummy” loads enabled us to include points where no actual load was applied. The calculation of a deflection jx can be simplified if the differentiation

with the respect to the load jP was carried out before the integration. In the case of a beam, referring to equation (1) and (2), the deflection of a beam can be wrote as

0

L

jj j

U M Mx dxP EI P∂ ∂

= =∂ ∂∫ (3)

Table 1 shows formula of horizontal and vertical deflection for few types of beam.

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SB/MMSB2/T2/BMCS2333/2

Table 1 Standard Formula to for horizontal and vertical deflection

Shape Dimensions Δ H Δ V

a) Semi circle

R = 150 mm

EIPR32

EIPR2

3π

b) Quarter circle

R = 150 mm

EIPR2

3

EIPR4

3π

c) Curved davit

R = 75 mm L = 150 mm

( )LREI

PRL+2

2

)4(4

2

RLEI

PRπ+

d) Angle davit

L1 = 150 mm L2 = 105 mm

EIPL

EILLLPL

62)707.0( 3

22121 ++

)3(6 21

22 LL

EIPL

+

P

P

P

PP

where, Young’s Modulus for aluminium alloy, Eal = 69 GNm-2 , P – load, R –radius, I – second moment of area and L - length APPARATUS a) Test Frame b) Back plate c) A pair of dial indicators d) Four test structures e) Weight set f) Vernier caliper

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SB/MMSB2/T2/BMCS2333/2

Figure 2 Test Frame PROCEDURES 1. Prepare the equipment to test the semicircle structure as the first test specimen. Ensure

that you have mounted and clamped securely the semicircle structure on each ends (refer Figure 1).

2. Measure and record the average width and thickness of the test structure cross section. Then calculate the second moment of area (I) of the cross section.

3. Attach the load hanger to the free end of the test structure. 4. Adjust the dial indicator in positions so it is in contact with the boss horizontally and

vertically. Ensure that the dial indicators can cover its maximum travel distance in each direction. Set the indicator reading to zero.

5. Apply a weight of 100 gm to the load hanger. Tap the test frame to reduce the effect of friction. Record the reading of both dial indicators.

6. Increase the weight up to 700 gm in 100 gm increments, tapping the test frame each time. Record the reading of both dial indicators. Record all loads and deflections reading in Table 2.

7. Repeat the above procedures with other structures (quarter circle, curved and angle davits).

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