Question

9-46. Sketch the influence line for the moment at D using the Müller-Breslau principle. Determine the maximum positive moment at D due to a uniform live load of 5 kN/m. El is constant. Assume A is a pin and B and C are rollers. 10 m -5 m

Answer 1

Solution given below :-

Given that

the ILD for moment at 'D'

Miller - Breslau principle :-

For moment at 'D' remove the moment restraint at the section but maintain axial and shear force resistance.

The moment resistance is eliminated by inserting hinge in the structure at section location.

The deflected shape gives ILD for moment at "D".

ILD for MD :-

For maximum positive moment at "D". Uniform in lead of 5kn/m is placed in BC portion.

Maximum positive moment at ‘D’

5 x (1 / 2 x 2.5 x 10)

62.5 KNM

MPM = 62.5 KNM