Influence line

structural theory I

1. INFLUENCE LINE For beams

2. INFLUENCE LINE FOR BEAMS Influence line shows graphically how the of a unit load across a structure influences some functions such as reactions , shears , moments , forces and deflections. Influence line maybe defined as a diagram whose ordinates show the magnitude and character of some function of a structure as a unit load moves across the structure. Each ordinate of the diagram gives the value of the function when the load is at that point.

3. Influence diagram is very useful for moving loads. It is used to determine where to place the loads to cause maximum values of a function and then compute those values INFLUENCE LINE FOR BEAMS

4. PROPERTIES OF INFLUNCE LINE 1. The value of a function due to a single concentrated moving load equals the magnitude of the load multiplied by the ordinate of the influence diagram. h Influence Diagram

5. PROPERTIES OF INFLUNCE LINE 2. The value of a function due to several concentrated moving loads equals the algebraic sum of the effects of each load described in property 1 h 1 Influence Diagram h 2 h 3 P 3 P 2 P 1

6. PROPERTIES OF INFLUNCE LINE 3. The value of a function due to a uniformly distributed load (w N/m) equals the product of w and the area of the influence line under the uniform load. w Influence Diagram Area

7. SCOPE Influence Line Diagram For REACTION SHEAR MOMENT STATICALLY DETERMINATE BEAMS

8. Drawing the INFLUENCE LINE Manually

9. Qualitative influence lines – a diagram showing the general slope of an influence line without the numerical value of its ordinate. Quantitative influence lines – an influence line with the numerical values of its ordinates known

10. Reaction Influence Line = Push the beam 1 unit at the point/support where reaction is studied. Then imagine how the beam will respond in coordination with the other supports within that beam. Drawing the INFLUENCE LINE Qualitatively Muller – Breslau’s Principle

11. 1 INFLUENCE LINE FOR REACTION A

12. Draw the Influence line for reaction at B by the same method earlier

13. PROBLEM SET

14. IMPORTANT NOTES IN TERMS OF UNIFORM LOADS, remember that we have uniform live load and uniform dead load.

15. Due to UNIFORM LIVE LOAD : The value of a response function due to a uniformly distributed live load over a potion of the structure can be obtained by multiplying the uniform live load by the area under corresponding portion of the influence line. The max positive value of a response function is equal to the uniform live load multiplied by the area over those portion of the structure where the ordinates of the influence line are positive . The max negative value. . . Opposite of the above mentioned rule

16. VALUE OF REACTION AT B when UNIFORM LIVE LOAD IS DISTRIBUTED ALL OVER THE SPAN VALUE OF MAXIMUM POSTIVE REACTION. (Value of maximum compressive reaction at column BG) The maximum negative value of a response function (Means – the maximum tensile reaction at column BG)

17. Due to UNIFORM DEAD LOAD : To obtain the value of a response function due to a uniform dead load, place the uniform dead load through out the entire span

18. Due to Combined uniform dead load, uniform live load and the live concentrated load : Requires analysis

19. The influence line for a given structure function is drawn above. If the structure is crossed by a distributed load of 30 kN /m with a length of 6 m, determine the maximum value of the function. 16 m 146.25 1

20. 12 m 4 m The influence line for a given structure function is drawn above. If the structure is crossed by a distributed load of 30 kN /m with a length of 6 m, determine the maximum value of the function. -0.75 0.25 -101.25

21. 12 m 4 m