MOLA exercise

In this exercise, you’re going to find influence lines using MOLA. It’s meant to give you insight in when these influence lines have straight and/or curved parts.

Components

We’ll use the following components:

MOLA	Model

Simply supported beam

Let’s start with the most basic model, a simply supported beam:

Fig. 4 Simply supported beam

Exercise (Simply supported beam)

Make the simply supported beam with MOLA

Solution to Exercise (Simply supported beam)

Exercise (Influence line vertical support reaction at A for simply supported beam)

Show the influence line of the vertical support reaction at A

Solution to Exercise (Influence line vertical support reaction at A for simply supported beam)

Exercise (Influence line vertical support reaction at B for simply supported beam)

Show the influence line of the vertical support reaction at B

Solution to Exercise (Influence line vertical support reaction at B for simply supported beam)

Exercise (Influence line bending moment for simply supported beam)

Show the influence line for the bending moment halfway the beam

Solution to Exercise (Influence line bending moment for simply supported beam)

Exercise (Influence line displacement for simply supported beam)

Show the influence line for the displacement halfway the beam

Solution to Exercise (Influence line displacement for simply supported beam)

Exercise (Influence line rotation for simply supported beam)

Show the influence line for the rotation halfway the beam

Solution to Exercise (Influence line rotation for simply supported beam)

Statically determinate hinged beam

Let’s increase complexity a bit, by looking at a statically determinate hinged beam:

Fig. 5 Statically determinate hinged beam

Exercise (Statically determinate hinged beam)

Make the statically determinate hinged beam with MOLA

Solution to Exercise (Statically determinate hinged beam)

Exercise (Influence line vertical support reaction at B for the statically determinate hinged beam)

Show the influence line of the vertical support reaction at B

Solution to Exercise (Influence line vertical support reaction at B for the statically determinate hinged beam)

Exercise (Influence line bending moment at D for the statically determinate hinged beam)

Show the influence line for the bending moment at D for the statically determinate hinged beam

Solution to Exercise (Influence line bending moment at D for the statically determinate hinged beam)

Exercise (Influence line bending moment at B for the statically determinate hinged beam)

Show the influence line for the bending moment at B for the statically determinate hinged beam

Solution to Exercise (Influence line bending moment at B for the statically determinate hinged beam)

Exercise (Influence line displacement in D for the statically determinate hinged beam)

Show the influence line for the displacement in D for the statically determinate hinged beam

Solution to Exercise (Influence line displacement in D for the statically determinate hinged beam)

Exercise (Influence line displacement in S2 for the statically determinate hinged beam)

Show the influence line for the displacement in S2 for the statically determinate hinged beam

Solution to Exercise (Influence line displacement in S2 for the statically determinate hinged beam)

Exercise (Influence line rotation in B for the statically determinate hinged beam)

Show the influence line for the rotation in B for the statically determinate hinged beam

Solution to Exercise (Influence line rotation in B for the statically determinate hinged beam)

Statically indeterminate hinged beam with stiff part

Let’s consider a statically indeterminate beam with an infinitive stiff part:

Fig. 6 Statically indeterminate hinged beam with stiff part

Exercise (Statically indeterminate beam with stiff part)

Make the statically indeterminate beam with stiff part with MOLA

Solution to Exercise (Statically indeterminate beam with stiff part)

Exercise (Influence line vertical support reaction at B for the statically indeterminate beam with stiff part)

Show the influence line of the vertical support reaction at B for the statically indeterminate beam with stiff part

Solution to Exercise (Influence line vertical support reaction at B for the statically indeterminate beam with stiff part)

Exercise (Influence line bending moment halfway AB for the statically indeterminate hinged beam with stiff part)

Show the influence line for the bending moment halfway AB for the statically indeterminate hinged beam with stiff part

Solution to Exercise (Influence line bending moment halfway AB for the statically indeterminate hinged beam with stiff part)

Statically indeterminate hinged beam

Finally, let’s consider another statically indeterminate hinged beam.

Fig. 7 Statically indeterminate hinged beam

Exercise (Statically indeterminate beam)

Make the statically indeterminate beam with MOLA

Solution to Exercise (Statically indeterminate beam)

Exercise (Influence line vertical support reaction at A for the statically indeterminate beam)

Show the influence line of the vertical support reaction at A for the statically indeterminate beam

Solution to Exercise (Influence line vertical support reaction at A for the statically indeterminate beam)

Exercise (Influence line bending moment at B for the statically indeterminate hinged beam)

Show the influence line for the bending moment at B for the statically indeterminate hinged beam

Solution to Exercise (Influence line bending moment at B for the statically indeterminate hinged beam)

Exercise (Influence line bending moment at D for the statically indeterminate hinged beam)

Show the influence line for the bending moment at D for the statically indeterminate hinged beam

Solution to Exercise (Influence line bending moment at D for the statically indeterminate hinged beam)