Question

Determine the slopes and deflections at points B and C for the beam shown below by the moment-area method. E=constant=70Gpa I=500 (10^6)mm^4

Answer 1

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answer :

Slopes : B = 180 mm , C = 373 mm

Deflection: B = 0.0514 rad , C = 0.077 rad

Step-by-step explanation:

Given data :

I = 500(10^6) mm^4

E = 70 GPa

The M / EI diagram is attached below

Deflection angle at B

∅B = ∅BA = [ 150 (6) + 1/2 (300)*6 ] / EI

= 1800 / ( 500 * 70 ) = 0.0514 rad

slope at B

ΔB = ΔBA = [ 150(6)*3 + 1/2 (300)*6*4 ] / EI

= 6300 / ( 500 * 70 ) = 0.18 m = 180 mm

Deflection angle at C

∅C = ∅CA = [ 1800 + 300*3 ] / EI

= 2700 / ( 500 * 70 )

= 2700 / 35000 = 0.077 rad

Slope at C

ΔC = [ 150 * 6 * 6 + 1/2 (800)*6*7 + 300(3) *1.5 ]

= 13050 / 35000 = 373 mm