Analyse the statically determinate beam illustrated below by expressing the load

Question

Analyse the statically determinate beam illustrated below by expressing the loading as a single function using Macaulay brackets and the Dirac delta, integrating to find the shear and axial forces and using statics to find the integration constants.  Integrate further to find the displacements, applying the boundary conditions appropriately. Find the shear force, bending moment, and displacement at point A taking displacement as positive upwards and using the internal convention for shear and moment. The cross section of the beam is constant with EI = 1100 kN.m2. a = 3.0 m, b = 2.5 m, c = 3.0 m and d = 0.5 m. w1 = 6 kN/m, w2 = 6 kN/m, and P = 19 kN.

Find

a) Shear force at point A (kN, internal convention): -19kN correct.

b) Moment at point A (kN.m, internal convention): -28.5 kNm correct.

c) Displacement at point A (mm, positive upwards: 1.256m is wrong answer.

Explanation / Answer

The value of C2 is wrong, you messed up the signs I guess it should be

721.5-384.5*9 = -2739

Thus displacement = -0.92m

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