Beam Reaction Apparatus.

EXPERIMENT NO. AIM: To verify the equilibrium of coplanar parallel forces with the help of beam reaction apparatus.

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THEORY Proposition 1: Condition of equilibrium. (∑magnitude of parallel forces =0) If a system of coplanar parallel forces acting on a body keeps it in equilibrium then the algebraic sum of magnitudes of the constituent force of the system is zero. General concept structure:

Coplanar parallel forces Equilibrium

Magnitude of parallel forces =0 Proposition 2: condition of equilibrium (moments of all parallel forces @ any point = 0) If a system of coplanar parallel forces acting of body keeps it in equilibrium , than the algebraic sum of moments of all the parallel forces about any point is zero

General concept structure:

Coplanar parallel Force system

equilibrium

∑Moments of all parallel

Forces @ any point = 0

APPARATUS: Beam Reaction apparatus, weights, weight hanger, string, meter scale and hooks.

DIAGRAM:

STEPWISE PROCEDURE: 1. Keep the Beam Reaction Apparatus on the table. 2. Measure the length of beam (span of a beam) between centres of two supports and note it in observations. 3. Measure the length of graduated parts of beam and note it in observations. 4. Determine least count of scale at supporting column indicating reaction of beam and note it in observations. 5. Note initial reactions as IR A and IRB at support A (left) and B (right) respectively with no load acting on beam and record it in observations. 6. Apply loads as parallel forces to hooks at any three locations and designating them as W1, W2 and W3 starting from left. Record magnitudes in observation table. 7. Measure the distances of these parallel forces W1, W2, and W3 from left support as X1, X2, and X3 respectively. Record distances in observation table. 8. Read the reactions at supports without removing forces W1, W2, and W3. Record them as final reactions FRA AND FRB at support A (left) and B (right) respectively in observation table. 9. Repeat the step 6, 7 and step 8 by changing magnitudes of forces and their position and take two more set of readings and record them in observation table.

OBSERVATIONS: 1. 2. 3. 4. 5.

Length of Beam (span) =L =.....................mm. Length of each graduated part = L / (No. Of parts) = .............../............=............... Least county of scale on supporting column =..............N Initial reaction at left support A =IR A = ...................N Initial reaction at right support B =IR B = ..................N

Table for calculation of reaction at support

Sr. No.

Parallel Forces (loads) in “N”

W1

W2

W3

Distances of  W1, W2 and W3 from left support “A” in mm X1 X2 X3

Observed reactions at support in “N” Support A

Support B

FRA

FRB

RA=(FRAIRA)

RB= (FRBIRB)

1 2 3

CLACULATIONS: For Reading no. .................... Reaction at support “A”, = (FR A –IRA) =.............. - ................ = ..............N Reaction at support “B”, = (FRB –IRB) =.............. - ................ = ..............N Algebraic sum of magnitudes all parallel forces:

- ve + ve ∑Magnitude of parallel forces =..................................................... ∑ FY = ........N Algebraic sum of moment of all parallel forces about point say “P” Sign convention: Clockwise moments ------ +ve Anti-Clockwise moments ------- -ve ∑Moments of parallel forces @ point “P” =∑ Mp ∑ Mp =............................................................. =...............................................................

RESULT: ∑ Fy =............................................................. ∑ Mp =.............................................................

CONCLUSION: For a system of parallel forces in equilibrium, the algebraic sum of all parallel forces is ........................................................... (equal to zero / nearly equal to zero). For a system of parallel forces in equilibrium, the algebraic sum of moment of all parallel forces about any point is........................................................... (equal to zero / nearly equal to zero).