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Muller -Bresalu principle states that, if we want to sketch the influence line for any force quantity (like thrust, shear, reaction, support moment or bending moment) in a structure,
(i) we remove from the structure the restraint to that force quantity
(ii) we apply on the remaining structure a unit displacement corresponding to that forces quantity.

**Muller Bresalu
principle**

Muller -Bresalu principle states that, if we want to sketch the influence line for any force quantity (like thrust, shear, reaction, support moment or bending moment) in a structure,

(i) we remove from the structure the restraint to that force quantity

(ii) we apply on the remaining structure a unit displacement corresponding to that forces quantity.

**For the two member determine bent in fig. sketch the influence line for VA.**

If we deftly apply Muller -Breslau to the problem, we can first remove support A and push A up by unit distance. Since the angle at B will remain unchanged, our unit displacement will result in a rigid body rotation of ?(=1/4 radian) about C. So the column CB will also have a horizontal displacement. (For the part AB, the diagram is just the influence line diagram for shear in a S.S beam)

The diagram for BC must be understood to be the influence of horizontal loads on the column on RA.

**principle on which indirect model analysis is based**

The indirect model analysis is based on the Muller Bresalu principle.

Muller Breslau principle has lead to simple method of using models of structures to get the influence lines for force quantities like bending moments, support moments, reactions, internal shears, thrusts, etc.

To get the influence line for any force quantity (i) remove the restraint due to the force, (ii) apply a unit displacement in the direction of the force.

**Begg's formeterde**

Begg'sdeformeter is a device to carry out indirect model analysis on structures. It has the facility to apply displacement corresponding to moment, shear or thrust at any desired point in the model. In addition, it provides facility to measure accurately the consequent displacements all over the model.

**'dummy length' modelsin tested with Begg'sformeterde.**

Dummy length is the additional length (of about 10 to 12 mm) left at the extremities of the model to enable any desired connection to be made with the gauges.

**Three types of connections possible with the model used with**

**Begg'sformeterde.**

(i) Hinged connection

(ii) Fixed connection

(iii) Floating connection

**Use of a micrometer microscope in model analysis with Begg's deformeter**

Micrometer microscope is an instrument used to measure the displacements of any point in the x and y directions of a model during tests with Begg'seformeterd.

**Name the types of rolling loads for which the absolute maximum bending moment occurs at the mid span of a beam.**

Types of rolling loads:

(i) Single concentrated load

(ii) Udl longer than the span

(iii) Udl shorter than the span

**Absolute maximum bending moment in a beam**

When a given load system moves from one end to the other end of a girder, depending upon the position of the load, there will be a maximum bending moment for every section. The maximum of these maximum bending moments will usually occur near or at the mid span. This maximum of maximum bending moment is called the absolute maximum bending moment,

Mmaxmax.

**The portal frame in fig. is hinged at D and is on rollers at A. Sketch the influence line for bending moment at B.**

To get the influence line diagram for MB, we shall introduce a hinge at B (and remove the resistance to bending moment). Now we get a unit rotation between BA and BC at B.

BC cannot rotate since column CD will prevent the rotation. BA would rotate freely (with zero moment). For ?=1 at B, displacement at A = 3m. The displaced position shows the influence line for MB as shown in fig.

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