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?
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.