Shear Force Balqis

SHEAR FORCE INFLUENCE LINES

1.0 OBJECTIVE

1.1 Part 1 : To plot shear force influence line.

1.2 Part 2 : To verify the use of a shear force influence on a simply supported

beam

2.0 LEARNING OUTCOMES

2.1 Able to apply the engineering knowledge in practical application

2.2 Able to enhance technical competency in structural engineering through

laboratory application.

2.3 Able to communication effectively in group.

2.4 Able to identify problem, solving and finding out appropriate solution

through laboratory application.

3.0 INTRODUCTION

Moving loads on beam are common features of design. Many road bridges

are constructed from beam, and as such have to be design to carry a knife edge

load, or a string of wheel loads, or a uniformly distributed load or perhaps the

worst combination of all three. The method of solving the problem is to use

influence line.

SHEAR FORCE INFLUENCE LINES

4.0 THEORY

Definition: Shear influence line is defined as a line representing the

changes in shear force at a section of a beam when a unit load moves on the beam.

Part 1 : This experiment examines how shear force varies at a cut section as a

unit load moves from one end to another (Figure 1). From the diagram, shear

force influence line equation can be written.

For 0 ≤ x ≤ a a shear line is given by:

Sy = -x / L………………..(1)

For a ≤ x ≤ b shear line is given by :

Sy = -x / L………………..(2)

SHEAR FORCE INFLUENCE LINES

Part 2 : If the beam are loaded as shown in Figure 2, the shear force at the ‘cut’

can be calculated using the influence line. (Diagram 2).

Shear force at ‘cut section’ = F1Y1 + F 2Y2 + F3Y3 …….(3)

(Y1 ,Y2 and Y3 are ordinates derived from the influence line in terms of x1, x2 , x3,

a, b and L

SHEAR FORCE INFLUENCE LINES

5.0 APPARATUS

6.0 PROCEDURES

5.1 Part 1

1. Check the Digital Force Meter reads zero with no load.

2. Place hanger with a 300g mass at the first grooved hanger support

at the left support and record the Digital Force reading in Table 1.

3. Repeat the procedure to next grooved hanger until to the last

grooved hanger at the right hand support.

4. Complete the calculation in Table 1.

5.1 Part 2

1. Place three load hangers with 100g, 200g and 300g mass

respectively at any position between the supports. Record the

position and the Digital Force Display reading in Table 2.

2. Repeat the procedure with three other locations.

3. Complete the calculation in Table 2.

SHEAR FORCE INFLUENCE LINES

7.0 RESULT

6.1 Part 1

6.1.1 Shear force at cut section is the same value given by Digital force

reading. Add negative sign to the value.

6.1.2 Experimental Influence line values =

Shear Force ( N )Load ( N )

6.1.3 Calculate the theoretical value using equation 1 for load position

40 to 260 mm and equation 2 for load position 320mm to 280mm.

Location of load from left hand

support (m)

Digital Force Display

Reading (N)

Shear Force at cut section (N)

Experimental Influence line

value

Theoretical Influence line

value

0.04 0.1 -0.1 -0.1 -0.09

0.06 0.2 -0.2 -0.2 -0.14

0.08 0.3 -0.3 -0.3 -0.18

0.10 0.4 -0.4 -0.4 -0.23

0.12 0.5 -0.5 -0.5 -0.27

0.14 0.6 -0.6 -0.6 -0.32

0.16 0.7 -0.7 -0.7 -0.36

0.18 0.8 -0.8 -0.8 -0.41

0.20 0.9 -0.9 -0.9 -0.45

0.22 1.0 -1.0 -1.0 -0.50

0.24 1.1 -1.1 -1.1 -0.55

0.26 1.1 -1.1 -1.1 -0.59

0.34 -0.5 0.5 0.5 0.23

0.36 -0.4 0.4 0.4 0.18

0.38 -0.3 0.3 0.3 0.14

0.40 -0.2 0.2 0.2 0.09

Table 1

SHEAR FORCE INFLUENCE LINES

Table 2

6.2 Part 2

6.2.1 Theoretical Shear Force is calculated using Equation 3.

Location Position of hanger from left hand support (m)

Shear force Digital

Reading (N)

Theoretical Shear (Nm)

100g 200g 300g1 0.36 0.10 0.18 1.4 -1.51

2 0.12 0.22 0.40 1.0 -1.00

3 0.36 0.20 0.08 1.3 -1.29

4 0.04 0.38 0.14 0.8 -0.77

SHEAR FORCE INFLUENCE LINES

8.0 DATA ANALYSIS

PART 1

For location 0.08m of load from left hand support,

Digital Force Reading = 0.3

Load (N) = 1 N

Shear Force at cut section = - (Digital force reading)

= - 0.3

Experimental Influence line values=

Shear Force ( N )Load ( N )

= - 0.3/1

= - 0.3

By using equation of Sy = -x/L

L = 0.44m

Theoretical influence line value (N) = - 0.08/0.44

= - 0.19

For location 0.20m of load from left hand support,

Digital Force Reading = 0.9

SHEAR FORCE INFLUENCE LINES

Load (N) = 1 N

Shear Force at cut section = - (Digital force reading)

= - 0.9

SHEAR FORCE INFLUENCE LINES

Experimental Influence line values=

Shear Force ( N )Load ( N )

= - 0.9/1

= - 0.9

By using equation of Sy = -x/L

L = 0.44m

Theoretical influence line value (N) = - 0.20/0.44

= - 0.45

PART 2

Calculation for theoretical shear (Nm)

Location 1

Position at hanger from left hand support (m)

100g (1N) → 0.36m y1 = 0.18

SHEAR FORCE INFLUENCE LINES

200g (2N) → 0.10m y2 = - 0.23

300g (3N) → 0.18m y3 = - 0.41

Shear Force at cut section

= F1Y1 + F 2Y2 + F3Y3

= 1(0.18) + 2(- 0.23) + 3( - 0.41)

= - 1.51 Nm

SHEAR FORCE INFLUENCE LINES

Location 2

Position at hanger from left hand support (m)

100g (1N) → 0.12m y1 = 0.27

200g (2N) → 0.22m y2 = - 0.50

300g (3N) → 0.40m y3 = 0.09

Shear Force at cut section

= F1Y1 + F 2Y2 + F3Y3

= 1(0.27) + 2(-0.50) + 3(0.09)

= - 1 Nm

Location 3

Position at hanger from left hand support (m)

100g (1N) → 0.36m y1 = 0.18

200g (2N) → 0.20m y2 = - 0.45

SHEAR FORCE INFLUENCE LINES

300g (3N) → 0.08m y3 = - 0.18

Shear Force at cut section

= F1Y1 + F 2Y2 + F3Y3

= 1(0.18) + 2(-0.45) + 3(-0.18)

= - 1.29 Nm

SHEAR FORCE INFLUENCE LINES

Location 4

Position at hanger from left hand support (m)

100g (1N) → 0.04m y1 = -0.09

200g (2N) → 0.38m y2 = 0.14

300g (3N) → 0.14m y3 = -0.32

Shear Force at cut section

= F1Y1 + F 2Y2 + F3Y3

= 1(0.09) + 2(0.14) + 3(-0.32)

= - 0.77 Nm

9.0 DISCUSSION

10.0 CONCLUSION

11.0 REFERENCES