Structural Analysis: Classification of Structures Unit 4 Part 1

Que2.11. bandy the pressure measure  system.

Answer  Pressure Measure Pressure measure for a member is defined as  the pressure per unit length of the member. It’s given by,  where, t =  Pressure measure,  T =  Pressure or pull in the member, and  l =  Length of the member.  Method of Tension Coefficient for Analysis of Plane Trusses  1. All the members of the stilt are  originally assumed to be under pressure  due to  cargo upon the stilt.  2. Let end A is at  knot i and end B is at  knot j, as shown inFig.2.11.1 and  let the pull in the member AB is Tij,  also at  knot ‘ i ’,( at point A)  where, lij =  Length of AB =  2 2  ij ij x y  3. also force at the  knot ‘ i ’ along Y direction, Ty =  tij × yij . Hence, if at  knot i there are more members and some external forces  are also present  also the condition of equilibrium at i can be written as,  Fx =  0  tijxij Fx =  0  tijxij tikxik tiqxiq. Fx =  0  and Fy =  0  tijyij Fy =  0  tijyij tikyik tiqyiq. Fy =  0  Where Fx is the external  cargo in the direction ofX-axis and Fy is the  external  cargo in the direction of Y- axis.  6. In case of a space stilt we have,

Que2.12. Explain in detail about  system of negotiation and   system of pressure measure with  exemplifications.

Answer  system of Negotiation  1. A complex stilt, as shown inFig.2.12.1, has three or  further connecting  members at a  knot, all with unknown member forces.  2. This precludes the use of the  system of sections or the  system of  resolution at the bumps as a means of determining the forces in the  stilt.  3. The  fashion consists of removing one of the being members at a   knot so that only two members with unknown forces remain and  substituting another member so as to maintain the stilt in stable  equilibrium.  4. The forces in member 4- 5 and 5- 9 are  attained by resolution of forces at   knot 5. still, at bumps 4 and 9, three unknown member forces  remain, and these can not be determined by resolution or by the  system  of sections.  5. As shown inFig.2.12.1( ii), member 3- 9 is removed, leaving only two  unknown forces at  knot 9, which may be determined.  6. To maintain stable equilibrium, a  cover member 3- 8 is added to   produce a modified stilt, and the original applied loads are applied to the  modified stilt.  7. The forces P in all the remaining members of the modified stilt may  now be determined. The force in member 3- 8 is P 3- 8.  8. The applied loads are now removed, and unit virtual loads are applied to  the modified stilt along the line of action of the original member 3- 9, as  shown inFig.2.12.1( iii).  9. The forces u in the modified stilt is determined; the force in member  3- 8 is – u3- 8.  10. Multiplying, the forces in system( iii) by P ′ 3 – 8/ u3 – 8 and adding them to  the forces in system( ii) gives the force in member 8 as  P3 – 8 =  P 3 – 8( – u3 – 8) P 3 – 8/ u3 – 8 =  0  11. In fact, the  cover member 3- 8 has been  excluded from the stilt.  Hence, by applying the principle of superposition, the final forces in the  original stilt are  attained from the expression  P =  P uP 3 – 8/ u3 – 8  where, tensile forces are positive and compressive forces are negative.

Que4.1. What do you understand by the term rolling loads?

Answer  1. Rolling Loads( or Moving Loads) In  factual practice, we  frequently   hassle with the loads which are moving or with positions that are  liable to change.  2. illustration Axle loads of moving  exchanges or vehicles, wheel loads of a   road train or wheel loads of a gantry assembly on a gantry girder   3. In case of rolling or moving loads it’s necessary to determine the  maximum shear force and bending moment at different sections as  the loads  cut  from one end to the other.

Que4.2. Define influence line  illustration. What are the advantages  of influence line and uses of it.

Answer  Influence Line Diagram  1. A  wind or graph that represents the function like a  response at support,  the shear force at a section, the bending moment at a section of a  structureetc., for  colorful positions of a unit  cargo on the span of the  structure is called an influence line  illustration for the function  represented.  2. For statically determinate structures, the influence lines for bending  moment, shear force or stress are composed of straight lines, while  they are curvilinear for statically indeterminate structures.  Advantages of Influence Lines Following are the advantages of  influence lines  1. still,  still, the  If a structure is  subordinated to a live  cargo or movingload.variation of the shear and bending moment in the member is stylish  described using the influence line.  2. Once the influence line is constructed, it’s easy to tell at a  regard  where the moving  cargo should be placed on the structure so that it  creates the  topmost influence at the specified point.  3. The magnitude of the associated  response, shear, moment or  deviation  at the point can be calculated from the ordinates of the influence line   illustration.  4. Influence lines play an important  part in the design of islands, artificial  crane rails, conveyors and other structures where loads move across  their span.  Uses of Influence Lines Following are the uses of influence lines  1. Influence lines are used to show the variation of shear force and  bending moment in the member which is  subordinated to a live  cargo or  moving  cargo.  2. Influence lines help to tell where the moving  cargo should be placed on  the structure so that it creates the  topmost influence at the specified  point.  3. Using the ordinates of influence line  illustration, the magnitude of  associated  response, shear, moment or  deviation at the point can be  calculated.  4. Influence lines are used to design the structures on which the loads  move across the span. The common types of structures are design of  islands, artificial crane rails and conveyorsetc.

Que4.4. bandy the maximum shear force and bending moment  at a section for a single concentrated  cargo moving over a ray.

Answer  Maximum SF and BM at a Section  1. Let W be the moving  cargo and the value of maximum SF and BM   needed be at C, which is at a distance z from A(Fig.4.4.1). ILD for SF  and BM are shown inFig.4.4.2 and4.4.3 independently.  2. FromFig.4.4.2, it’s clear that maximum negative SF occurs when the   cargo is just to the left wing of section C and its value is =   3. also, maximum positive SF occurs when the  cargo is just to the  right of the section and its value is =  L z  4. From ILD for moment MC, it’s clear that maximum bending moment  will  do when the  cargo is on the section itself and its value is.

Que4.5. What will be the value of maximum shear force and  bending moment at a section for a slightly distributed  cargo longer  than the span?

OR

Draw and determine the maximum value of shear force and bending  moment for a rolling UDL longer than the span of the girder.

Answer  Maximum SF and BM at given Section  1. Let a slightly distributed  cargo of intensity w move from left to right.  cargo intensity times the area of ILD over loaded length gives the value  of stress attendant( SF). pertaining again toFig.4.4.2.  2. Negative SF is maximum, when the  cargo covers portion AC only.  Maximum negative SF, SC =  w × Area of ILD for SC in length AC . Positive SF is maximum, when the slightly distributed  cargo occupies  the portion CB only.