9.Influence

9.Influence - Theory and Design of Structures I Influence...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Theory and Design of Structures I Influence Lines Influence Lines Moving Loads • In static, constant and stationary loads, the reactions, stresses and deformations at a particular section are constant • However, the load effects become variable functions of the position of the load when the loads are moving, even if the dynamic effects are ignored Influence Lines • Examples of moving loads: – locomotives rolling on a railway bridge – motor vehicles speeding over flyovers – occupants moving in a building • Two structural problems arise: – position of the live load that will cause the maximum effect at a certain section – magnitude of the maximum effect Influence Lines • An influence line is a graph or chart showing the value of some direct linear function (reaction, shear, bending moment, axial force, etc) at a certain point in the structure due to a unit concentrated load moving across the span • It illustrates the variation of the effect Q (reaction, stress) at a fixed point i due to a moving unit cause (unit force or moment) acting at a moving position j Use of Influence Lines Use of Influence Lines • It provides a tool for determining the maximum load effect. There are 3 different cases in determination of the value of the effect Q at a fixed point i: – Single concentrated moving load – System of concentrated moving loads – Uniformly distributed moving load P = 1 i j z(j) j ) ( j z P Q i ⋅ = i P ∑ ⋅ = j j j i z P Q i P 3 P 1 P2 z 1 z 2 z 3 ∫ ⋅ = = A p pzdx Q i i p z A d P = 1 i j z(j) j ) ( j z P Q i ⋅ = i P Single concentrated moving load Influence line due to unit load System of concentrated moving loads P = 1 i j ∑ ⋅ = j j j i z P Q i P 3 P 1 P 2 z 1 z 2 z 3 Uniformly distributed moving load P = 1 i j ∫ ⋅ = = A p pzdx Q i i p z A d Influence Lines for Beams Consider a simply supported beam with overhang as shown A B D C 4m 4m 16m Moving unit load R B 1.25 A B D C 4m 4m 16m x P = 1 I.L. for reaction at B, R B • Imagine a unit load P starts at C and moves towards B and A so that distance x of the load from C is varying. Taking moment about C for the whole beam, Px L R B = 16 x R B = 20 ≤ ≤ x I.L. for R B R B R B 1.25 A B D C 4m 4m 16m x P = 1 I.L. for reaction at B, R B When P is at C, When P is at B, When P is at A, , = = B R x 1 , 16 = = B R x 25 . 1 , 20 = = B R x I.L. for R B R B I.L. for reaction at B, R B I.L. for reaction at C, R C • Imagine a unit load P moves from A to C so that x is the distance of P to the right of B. Taking moment about B for the whole beam, R C (16) = P x R C = x /16 for -4 ≤ x ≤ 16 1.0 R C-0.25 A B D C 4m 4m 16m x P = 1 I.L. for R C R C...
View Full Document

This note was uploaded on 12/01/2010 for the course CIVL 2007 taught by Professor Profchai during the Spring '10 term at HKU.

Page1 / 12

9.Influence - Theory and Design of Structures I Influence...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online