Influence Line DiagramsII Theory of Structures I 1

Contents l Qualitative Influence Lines l Influence lines for Girders l Influence Lines for

Qualitative Influence Lines l l In 1886, Heinrich Muller-Breslau developed a technique for rapidly

In order to draw deflected shape properly, the capacity of the beam to resist

Proof: Reaction Work = Force. Displacement = Moment. Rotational displacement 1 1 y ’

MOMENT 1 C Mc Deflected Shape Mc 1 y ’ 9

Practice Problems l Example 6 -9 to 6 -12 l Chapter 6 l Structural

l l Unit load on the slab is transferred to the girder only at

l l l Moment will depend on where the point p is located but

l Since the girder is affected only by the loadings transmitted by the floor

x 0 10 20 30 40 VCD 0. 333 0 -0. 333 0 23

Practice Problems l Example 6 -13 to 6 -14 l Chapter 6 l Structural

Truss top cord sway bracing top lateral bracing portal bracing stringers portal end post

x FGB 0 0 10 0. 354 20 -0. 707 30 -0. 354 40

Practice Problems l Example 6 -15 to 6 -17 l Chapter 6 l Structural

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Influence Line Diagrams-II Theory of Structures - I 1

Contents l Qualitative Influence Lines l Influence lines for Girders l Influence Lines for Trusses 2

Qualitative Influence Lines l l 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” 3

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. l Ay REACTION A A Ay x Influence line for Ay 4

SHEAR C Vc Deflected Shape Vc 5

MOMENT C Deflected Shape 6

Proof: Reaction Work = Force. Displacement = Moment. Rotational displacement 1 1 y ’ y C A C x Ay 7

SHEAR 1 C 1 Vc y ’ Vc 8

MOMENT 1 C Mc Deflected Shape Mc 1 y ’ 9

Example 6 -9 10

Practice Problems l Example 6 -9 to 6 -12 l Chapter 6 l Structural Analysis by R C Hibbeler 13

Influence Lines for Girders 14

l l 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. 15

l l l 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. 19

l Since the girder is affected only by the loadings transmitted by the floor beams, the unit load is generally placed at each floorbeam location to establish the necessary data used to draw the influence line. 20

Example 6 -13 21

x 0 10 20 30 40 VCD 0. 333 0 -0. 333 0 23

Practice Problems l Example 6 -13 to 6 -14 l Chapter 6 l Structural Analysis by R C Hibbeler 24

Truss top cord sway bracing top lateral bracing portal bracing stringers portal end post deck panel bottom cord floor beam 25

Example 6 -15 26

x FGB 0 0 10 0. 354 20 -0. 707 30 -0. 354 40 0 28

Practice Problems l Example 6 -15 to 6 -17 l Chapter 6 l Structural Analysis by R C Hibbeler 29