What is the section modulus for a rectangular section?

What is the section modulus for a rectangular section?

What is the section modulus (Z) for a rectangular section? Explanation: The modulus of section may be defined as the ratio of moment of inertia to the distance to the extreme fibre. It is denoted by Z. Z= I/y ; For rectangular section, I = bd3/12 & y = d/2.

How do you find the modulus of a hollow rectangle?

The elastic section modulus is defined as S = I / y, where I is the second moment of area (or area moment of inertia, not to be confused with moment of inertia) and y is the distance from the neutral axis to any given fibre.

What is ZX in steel design?

3 Zx represents the plastic section. modulus about the X-axis of a shape, where the full cross-section of the shape has yielded.

How is plastic modulus of I section calculated?

The plastic section modulus for a rectangular cross section can be determined by multiplying each section half (e.g., the shaded area shown in Figure 1.

What is the difference between plastic and elastic section modulus?

The plastic section modulus assumes the entire section yields. Elastic modulus is the steel modulus based on the stress strain curve before yielding. The plastic modulus is after yielding. If the failure is considered till the elastic zone then we consider elastic modulus.

What is plastic moment resistance?

It is defined as the moment at which the entire cross section has reached its yield stress. This is theoretically the maximum bending moment that the section can resist - when this point is reached a plastic hinge is formed and any load beyond this point will result in theoretically infinite plastic deformation.

How do you find plastic moments?

Find the location of the plastic neutral surface: Divide the cross sectional area into two areas, At and Ac, such that At = Ac. Find the distance, L, between the centroids of the two areas. The plastic moment is Mp = σy · L · Ac.

What is difference between plastic design and elastic design?

Plastic design is known to be a displacement-based method in which a pre-selected target drift is used along with yield mechanisms as a part of the design criteria. On the other hand, elastic designs are usually based on the conventional force based limit state method.

What is static theorem?

Lower Bound Theorem [P] (Static Theorem) An external load computed on the basis of an assumed distribution of internal forces, in which. • the forces are bounded by limit values, and • the forces are in equilibrium, is less than or equal to the true collapse load.

What is difference between plastic hinge and mechanical hinge?

What is difference between plastic hinge and mechanical hinge? ... The only difference is that plastic hinges permit rotation with a constant resisting moment equal to the plastic moment Mp. At mechanical hinges, theresisting moment is equal to zero.

What is static theorem Mcq?

1. What is static theorem ? Explanation: For a given frame and loading if there exists any distribution of bending moments throughout the frame which is both safe and statically admissible with set of load P, then value of load P must be less than or equal to collapse load. 2.

What is the condition of equilibrium in plastic analysis?

Explanation: When equilibrium and plasticity conditions of plastic analysis are satisfied, an lower bound solution of true ultimate load is obtained.

What is beam plastic hinge?

A plastic hinge, in structural engineering, refers to the deformation of a part of a beam wherever plastic bending happens. Hinge means that having no capability to resist moment. Therefore, a plastic hinge behaves like a standard hinge - permitting free rotation.

How many linear displacements can a node have in a 2 dimensional frame beam?

2 displacements

What is plastic design?

Plastic design is a method by which structural elements are selected considering the system's overall ultimate capacity. For safety, the applied loads are in- creased by load factors dictated by appropriate codes. ... Plastic design is based on the behavior of steel in the range 2-3.

What are the common design rules in plastic design?

Here are 8 important factors to consider to meet your plastic part design goals for a successful production process.

  • Material Considerations. ...
  • Radius. ...
  • Wall Thickness. ...
  • Gate Location. ...
  • Draft. ...
  • Inclusion of Ribs. ...
  • Mold Shrinkage. ...
  • Special Features.

What is plastic theory?

Plastic Theory of Structures focuses on the use of plastic theory in design and shows how code requirements are related to theoretical considerations. ... Attention is paid to how the collapse load factor of a given structure may be derived, that is, the structure has been analyzed in relation to plastic collapse.

What is collapse load?

The applied load at which a structure becomes a mechanism owing to the formation of sufficient plastic hinges for collapse to occur. ... ...

What is the plastic collapse load?

Explanation: The load at which sufficient number of plastic hinges are formed in a structure such that a collapse mechanism is created is called plastic-collapse load or plastic-limit load.

What is collapse mechanism?

Definition - What does Collapse Mechanism mean? By inserting a plastic hinge at a plastic limit load into a statically determinate beam, a kinematic mechanism permitting an unbounded displacement of the system can be formed. This is known as the collapse mechanism.

What is beam mechanism?

Beam mechanism—when vertical loads are applied to beams and horizontal loads to columns to form partial collapse mechanisms as shown in Figure 5.

How many plastic hinges are required to convert the structure into a mechanism?

– The number of plastic hinges required for failure of statically indeterminate structure will be shown to vary from structure to structure, but never be less than two.

What is plastic hinge length?

The plastic hinge length is defined as the length over a seismically swaying column, where flexural moments exceed the yielding capacity. ... The latter is meant to account in a simplistic manner for the effects of bar yielding penetration from the critical section towards both the shear span and the support of columns.

What is shape factor in plastic analysis?

The shape factor of the cross-section shape shall be considered which is the ratio of plastic to elastic moment and it is different for each shape. For example, the shape factor for rectangular shape is 1.

Can shape factor be less than 1?

Shape factors are often normalized, that is, the value ranges from zero to one. ... A shape factor equal to one usually represents an ideal case or maximum symmetry, such as a circle, sphere, square or cube.