Influence Lines | Structural Analysis - Civil Engineering (CE) PDF Download

Unfluence Line Diagram and Rolling Loads

Influence Line Diagram represents variation in the values of a particular stress function such as reactions, SF, BM, axial force, slope or deflections etc, when a unit concentrated load moves from one end to the other end of span.

The ordinate of influence line at any section (say y₁) represents magnitude of that stress function when unit concentrated load is placed at that section
(i)

(ii)

Total vertical reactions RB due to given load system is
R_B = P₁Y₁ + P₂Y₂ + wA

(iii)

ILD for shear force at C

(iv)

ILD for Bending Moment at C

(v)

BM_max at C = P. ab/l + wA

(vi)

Position of load for maximum positive SF at C 

Position of load for maximum negative SF at C 

(vii)

Position of load for maximum positive SF at C

Maximum positive SF at C = wA₁
Maximum negative SF at C = wA₂

Simply Supported Beam with Overhang

Simply Supported Beam Carrying Internal Hinge

Effect of rolling loads

To find maximum SF and BM at section C when a UDL passes over the girder from let to right having length less then length of girder.

Length of load is l' (<L)

1. The maximum negative shear force at section C will be, when head of the load is just to the left of section and loaded part is AC.Maximum negative shear force at C = w x artea of ILD below loading
2. Maximum positive shear force at C will occur when tail of load is just to the right of C.
3. Maximum BM at C will occur when average loading just to the left of C = average loading just to the right of C. It means section C will devide load in the same ratio as it devides to the span.

Influence line diagram for truss members

ILD for Inclined members