Mos module 2(SFD and BMD)
- 1. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Concept of Axial force:- If the load is applied through the center of gravity of its cross section, it is called an axial load. Axial force is the compression or tension force acting in a member. If the axial force acts through the centroid of the member it is called concentric loading. If the force is not acting through the centroid it’s called eccentric loading. Eccentric loading produces a moment as a result of the load being a distance away from the centroid.
- 2. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Concept of shear force:- In the simple words shear force can be defined as unbalanced lateral force across section of element. 10KN 5 KN Shear force=10-5=5KN
- 3. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Concept of bending moment:- A bending moment is a force normally measured in a force x perpendicular distance (e.g. kNm). Bending moments occur when a force is applied at a given distance away from a point of reference; causing a bending effect. In the most simple terms, a bending moment is basically a force that causes something to bend. If the object is not well-restrained the bending force will cause the object to rotate about a certain point. Example:- Bending moment at point A=10X0.2=2Nm It is important to note that to use the adjacent formula, the force (in this case a 10 N downward force) must NOT pass through the point. This is obvious as if we applied the same formula (distance x force) the distance would equal zero and therefore there would be no bending moment.
- 4. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Types of load:- 1. Concentrated or point load(P):- a concentrated load is one which is considered to act at a point. 2. uniformly distributed load (UDL):-it is a load that is distributed or spread across the whole region of an element such as a beam or slab. In other words, the magnitude of the load remains uniform throughout the whole element.
- 5. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Types of support:- Supports are arguably one of the most important aspects of a structure, as it specifies how the forces within the structure are transferred to the ground. 1. Fixed support:- It is the most rigid type of support or connection. It constrains the member in all translations and rotations (i.e. it cannot move or rotate in any direction). The easiest example of a fixed support would be a pole or column in concrete. The pole cannot twist, rotate or displace; it is basically restricted in all its movements at this connection. Fixed supports are extremely beneficial when you can only use a single support. The fixed support provides all the constraints necessary to ensure the structure is static. It is most widely used as the only support for a cantilever. No of reaction:-3
- 6. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Types of support:- 2. Pinned support(hinge support):-it is a very common type of support and is most commonly compared to a hinge in civil engineering. Like a hinge, a pinned support allows rotation to occur but no translation (i.e. it resists horizontal and vertical forces but not a moment). No of reaction:-2
- 7. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Types of support:- 4. simple support :-It is basically just where the member rests on an external structure. They are quite similar to roller supports in a sense that they are able to restrain vertical forces but not horizontal forces. The member simply rests on an external structure to which the force is transferred to. In this case, if you apply a vertical force it will not be able to support it. An example is a plank of wood resting on two concrete blocks. The plank can support any downward (vertical) force but if you apply a horizontal force, the plank will simply slide off the concrete blocks. Simple supports aren't widely used in real life structures unless the engineer can be sure that the member will not translate; otherwise they run the risk of the member simply falling off the support. No of reaction:-1 Ry
- 8. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Sign convention:-(SFD) The shear force at a section will be considered positive when resultant of the forces to the left of the section is upwards or to the right of the section is downwards, similarly The shear force at a section will be considered negative when resultant of the forces to the left of the section is downwards or to the right of the section is upwards + ve - ve
- 9. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Sign convention:-(BMD) The bending moment will be considered positive when the moment of the forces and reactions on left portion is clockwise and right portion anti-clockwise, similarly The bending moment will be considered negative when the moment of the forces and reactions on left portion is anti- clockwise and right portion is clockwise + ve - ve
- 10. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES SFD and BMD of statically determinate simply supported beam(point load) Statically determinate structure:- The structure which can be analyzed with the help of equations of static equilibrium. Equation of static equilibrium:- 1. Summation of forces in x direction=0 2. Summation of forces in y direction=0 3. Summation of moment about z direction=0 Example of statically determinate structure- a simply supported beam, cantilever beam • How to determine static indetermancy:- • static indetermancy= no of reaction-equation of static equilibrium = R-3 Si=R-3 =3-3 =0 Si=R-3 =3-3 =0
- 11. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES Typical SFD and BMD Diagram Loading SF BM No variation Constant(X^0) Constant (x^0) (x^1) linear inclined (x^1) linear inclined (x^2) Parabola (x^1) linear inclined (x^2) Parabola (x^3) Parabola
- 12. AF, SF AND BMD FOR BEAMS AND PORTAL FRAMES SFD and BMD of statically determinate simply supported beam and cantilever beam 1. https://youtu.be/ZOwyRMGsLZ8 2. https://youtu.be/kjqP71kfJmw 3. https://youtu.be/Y_jwfpcgy10 4. https://youtu.be/WKiFFEqm9EI 5. https://youtu.be/kAuetQWzurw