Plastic Analysis · Structural Analysis · GATE CE

For the square steel beam cross-section shown in the figure, the shape factor about Z - Z axis is S and the plastic moment capacity is M_p. Consider yield stress f_y = 250 MPa and a = 100 mm.

The values of S and M_p (rounded off to one decimal place) are

Match the information given in Group $$-$$ $${\rm I}$$ with those in Group $$-$$ $${\rm II}.$$

The ultimate collapse load $$(P)$$ in terms of plastic moment $${M_P}$$ by kinematic approach for a propped cantilever of length $$L$$ with $$P$$ acting at its mid-span as shown in the figure, would be

As per $$IS$$ $$800:2007$$ the cross-section in which the extreme fiber can reach the yield stress, but cannot develop the plastic moment of resistance due to failure by local buckling is classified as

In the theory of plastic bending of beams, the ratio of plastic moment to yield moment is called

The shape of the cross-section, which has the largest shape factor, is

For a fixed beam with span $$L,$$ having plastic moment capacity of $${{M_p}}$$, the ultimate central concentrated load will be

If $$'YY'$$ is the centroidal axis of a $$T$$-beam section, subjected to plastic moment, $${M_P},$$ the neutral axis lies

Equilibrium condition, yield conditions $$\left( {M \le {M_p}} \right)$$ and mechanism condition (formation of a plastic collapse mechanism) are the conditions to be satisfied by any correct plastic analysis results. Which of the above conditions does the statical methods of plastic analysis consider?

Number of independent displacement modes (sway mechanisms) for the given frame with the load shown there in are

The number of independent mechanisms the gable frame will have when loaded as shown is

A fixed-end beam is subjected to a concentrated load $$(P)$$ as shown in the figure. The beam has two different segments having different plastic moment capacities $$\left( {{M_P},\,2{M_P}} \right)$$ as shown.

The minimum value of load $$(P)$$ at which the beam would collapse (ultimate load) is

A propped cantilever of span $$L$$ carries a vertical concentrated load at the mid-span. If the plastic moment capacity of the section is $${M_P}$$, the magnitude of the collapse load is

A fixed end beam is subjected to a load, W at $$1/3rd$$ span from the left support as shown in the figure. The collapse load of the beam is

For formation of collapse mechanism in the following figure, the minimum value of $${{P_u}}$$ is $$c{M_P}/L.$$ $${M_P}$$ and $$3{M_P}$$ denote the plastic moment capacities of beam sections as shown in this figure. The value of $$c$$ is ________.

A prismatic beam (as shown below) has plastic moment capacity of $${{M_P}}$$, then the collapse load $$P$$ of the beam is

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load $$P$$ at mid span as shown.

If load $$P=80$$ $$kN,$$ find the reaction ܴ$$R$$ (in $$kN$$) (correct to $$1$$-decimal place)using elastic analysis ___________

A propped cantilever made of a prismatic steel beam is subjected to a concentrated load $$P$$ at mid span as shown.

If the magnitude of loadܲ is increased till collapse and the plastic moment carrying capacity of steel beam section is $$90$$ $$kN$$-$$m$$, ݇ܰ݉determine reaction ܴ$$R$$(in ݇ܰ$$kN$$)(correct to $$1$$-decimal place) using plastic analysis. ____________

The value of $$W$$ that results in the collapses of the beam shown in the adjoining figure and having a plastic moment capacity of $${M_P}$$ is

A continuous beam is loaded as shown in the figure below. Assuming a plastic moment capacity equal to $${{M_P}}$$, the minimum load at which the beam would collapse is

The plastic collapse load $${{W_P}}$$ for the propped cantilever supporting two point loads as shown in the figure in terms of plastic moment capacity, $${{M_P}}$$ is given by

When the triangular section of a beam as shown below becomes a plastic hinge, the compressive force acting on the section (with $${\sigma _y}$$ denoting the yield stress) becomes

A cantilever beam of length $$l,$$ width $$b$$ and depth $$d$$ is loaded with a concentrated vertical load at the tip. If yielding starts at a load $$P,$$ the collapse load shall be

A steel portal frame has dimensions, plastic moment capacitance and applied loads as shown in the figure. The vertical load is always twice of the horizontal load. The collapse load $$P$$ required for the development of a beam mechanism is

A steel beam (with a constant $$EI,$$ and span $$L$$) is fixed at both ends and carries a uniformly distributed load ($$w$$ $$kN/m$$), which is gradually increased till the beam reaches the stage of plastic collapse (refer to the following figure). Assuming $$'B'$$ to be at mid-span, which of the following is true.

The four cross sections shown below are required to be ordered in the increasing order of their respective shape factors.

A cantilever beam of length $$L$$ and a cross section with shape factor $$'f'$$ supports a concentrated load $$P$$ as shown below:

The length $${L_P}$$ of the plastic zone, when the maximum bending moment, equals the plastic moment $${M_P}$$, given by

The shape factor of the section shown in fig. is

The plastic modulus of a section is $$4.8 \times {10^{ - 4}}\,\,{m^3}.$$ The shape factor is $$1.2$$. The plastic moment capacity of the section is $$120$$ $$kN$$-$$m.$$ The yield stress of the material is

The fixed beam $$AB$$ has a span of $$3000$$ $$mm$$ and is of uniform cross-section. The plastic moment capacity $$({M_P})$$ of the beam's cross-section is $$1.5 \times {10^8}\,\,N$$-$$mm.$$

The beam will have like a simply supported beam when the magnitude of distributed load $$P$$ attains a value equal to:

A Propped cantilever beam is shown below. The plastic moment capacity of the beam is $${M_P}.$$ The collapse load is

Calculate the shape factor for the $$T$$-section shown in the following figure made up of two plates $$100\,\,mm \times 10\,\,mm.$$ What will be the load factor if the permissible stress in bending is only $$2/3$$ of the yield stress $$\left( {{\sigma _y}} \right)$$

The steel portal frame shown in figure is subjected to an imposed service load of $$15$$ $$kN$$. Compute the required plastic moment capacity of the members. All the members are of the same cross-section. Draw the collapse load.