Influence Line Diagrams-II Theory of Structures - I

Contents Qualitative Influence Lines Influence lines for Girders Influence Lines for Trusses

Qualitative Influence Lines In 1886, Heinrich Muller-Breslau developed a technique for rapidly constructing influence lines. It states “the influence line for a function (reaction, shear or moment) is to be the same scale as the deflected shape of the beam when the beam is acted upon by that function”

In order to draw deflected shape properly, the capacity of the beam to resist the applied function must be removed so the beam can deflect when the function is applied. Ay REACTION A A Ay x Influence line for Ay

SHEAR C Vc Deflected Shape Vc

MOMENT C Deflected Shape

Proof: Reaction Work = Force . Displacement = Moment . Rotational displacement 1 1 y’ y C C x A Ay

SHEAR 1 C Vc 1 y’ Vc

MOMENT 1 C  Mc Mc 1 y’ Deflected Shape

Example 6-9

Practice Problems Example 6-9 to 6-12 Chapter 6 Structural Analysis by R C Hibbeler

Influence Lines for Girders

Unit load on the slab is transferred to the girder only at points where it is in contact with the floor beams. A, B, C and D are panel points and the region between these points is known as panel.

Moment will depend on where the point p is located but shear will remain same in the whole panel. Influence line for shear in floor girders are specified for panels in the girder and not specific points along the girder. Shear is referred to panel shear.

Since the girder is affected only by the loadings transmitted by the floor beams, the unit load is generally placed at each floor-beam location to establish the necessary data used to draw the influence line.

Example 6-13

x VCD 0.333 10 20 -0.333 30 40

Practice Problems Example 6-13 to 6-14 Chapter 6 Structural Analysis by R C Hibbeler

Truss top cord sway bracing top lateral bracing portal bracing deck stringers bottom cord portal end post panel floor beam

Example 6-15

x FGB 10 0.354 20 -0.707 30 -0.354 40

Practice Problems Example 6-15 to 6-17 Chapter 6 Structural Analysis by R C Hibbeler

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