Singly Reinforced Sections · Reinforced Cement Concrete · GATE CE

Consider a reinforced concrete beam section of 350 mm width and 600 mm depth. The beam is reinforced with the tension steel of $800 \mathrm{~mm}^2$ area at an effective cover of 40 mm . Consider M20 concrete and Fe415 steel. Let the stress block considered for concrete in IS 456:2000 be replaced by an equivalent rectangular stress block, with no change in (a) the area of the stress block, (b) the design strength of concrete (at the strain of 0.0035), and (c) the location of neutral axis at flexural collapse. The ultimate moment of resistance of the beam (in kN.m) is __________ (round off to the nearest integer).

GATE CE 2025 Set 2

Consider a reinforced concrete beam section of 300 mm width and 700 mm depth. The beam is reinforced with the tension steel of $2000 \mathrm{~mm}^2$ area at an effective cover of 50 mm . Concrete in the tension zone is assumed to be cracked. Assume the modular ratio of 12 and Young's modulus of 200 GPa for steel. When the extreme fibre in the compression zone undergoes the strain of 0.0004 due to the applied bending moment, the stress in the steel (in MPa ) is _________ (rounded off to the nearest integer).

GATE CE 2025 Set 1

Consider the singly reinforced section of a cantilever concrete beam under bending, as shown in the figure (M25 grade concrete, Fe415 grade steel). The stress block parameters for the section at ultimate limit state, as per IS 456: 2000 notations, are given. The ultimate moment of resistance for the section by the Limit State Method is ________ kN.m (round off to one decimal place).

[Note: Here, As is the total area of tension steel bars, b is the width of the section, d is the effective depth of the bars, f_ck is the characteristic compressive cube strength of concrete, f_y is the yield stress of steel, and x_u is the depth of neutral axis.]

GATE CE 2023 Set 2

A reinforced concrete $$(RC)$$ beam with width of $$250$$ $$mm$$ and effective depth of $$400$$ $$mm$$ is reinforced with $$Fe415$$ steel. As per the provisions of $$IS$$ $$456$$ - $$2000,$$ the minimum and maximum amount of tensile reinforcement (expressed in $$m{m^2}$$ ) for the section are, respectively

GATE CE 2016 Set 1

Consider the singly reinforced beam section given below (left figure). The stress block parameters for the cross-section from $$IS:$$ $$456$$ - $$2000$$ are also given below (right figure). The moment of resistance for the given section by the limit state method is ______ $$kN$$-$$m.$$

GATE CE 2015 Set 1

For a beam of cross-section, width $$= 230$$ $$mm$$ and effective depth $$= 500$$ $$mm,$$ the number of rebars of $$12$$ $$mm$$ diameter required to satisfy minimum tension reinforcement requirement specified by $$IS:$$ $$456-2000$$ (assuming grade of steel reinforcement as $$Fe500$$) is _______________

GATE CE 2014 Set 1

In a reinforced concrete section, the stress at the extreme fibre in compression is $$5.80$$ $$MPa.$$ The depth of neutral axis in the section is $$58$$ $$mm$$ and the grade of concrete is $$M25.$$ Assuming linear elastic behavior of the concrete, the effective curvature of the section (in per $$mm$$) is

GATE CE 2014 Set 1

A singly reinforced rectangular concrete beam has a width of $$150$$ $$mm$$ and an effective depth of $$330$$ $$mm.$$ The characteristic compressive strength of concrete is $$20$$ $$MPa$$ and the characteristic tensile strength of steel is $$\,\,\,\,\,\,\,415\,\,MPa.$$

Adopt the stress block for concrete as given in $$IS$$ $$456$$-$$2000$$ and take limiting value of depth of neutral axis as $$0.48$$ times the effective depth of the beam.

The limiting value of the moment of resistance of the beam in $$kN$$-$$m$$ is

GATE CE 2007

Adopt the stress block for concrete as given in $$IS$$ $$456$$-$$2000$$ and take limiting value of depth of neutral axis as $$0.48$$ times the effective depth of the beam.

The limiting area of tension steel in $$m{m^2}$$ is

GATE CE 2007

In the design of beams for the limit state of collapse in flexure as per $$IS:$$ $$456$$ - $$2000,$$ let the maximum strain in concrete be limited to $$0.0025$$ (in place of $$0.0035$$). For this situation, consider a rectangular beam section with breadth as $$250$$ $$mm,$$ effective depth as $$350$$ $$mm,$$ area of tension steel as $$1500\,\,m{m^2},$$ and characteristic strengths of concrete and steel as $$30$$ $$MPa$$ and $$250$$ $$MPa$$ respectively.

The depth of neutral axis for the balanced failure is

GATE CE 2006

Consider the following statements:

$$1.\,\,\,\,\,\,$$ The width-to-thickness ratio limitations on the plate elements under
$$\,\,\,\,\,\,\,\,\,\,\,$$ compression in steel members are imposed by $$IS:$$ $$800$$ - $$1984$$ in order to avoid
$$\,\,\,\,\,\,\,\,\,\,\,$$ fabrication difficulties.
$$2.\,\,\,\,\,\,$$ In a doubly reinforced concrete beam, the strain in compressive reinforcement is
$$\,\,\,\,\,\,\,\,\,\,\,$$ higher than the strain in the adjoining concrete.
$$3.\,\,\,\,\,\,$$ If a cantilever $${\rm I}$$-section supports slab construction all along its length with
$$\,\,\,\,\,\,\,\,\,\,\,$$ sufficient friction between them, the permissible bending stress in compression
$$\,\,\,\,\,\,\,\,\,\,\,$$ will be the same as that in tension.

The TRUE statements are

GATE CE 2006

At the limiting state of collapse in flexure, the force acting on the compression zone of the section is

GATE CE 2006

Maximum strains in an extreme fibre in concrete and in the tension reinforcement (Fe-$$415$$ grade and $${E_s} = 200\,\,kN/m{m^2}$$) in a balanced section at limit state of flexure are respectively

GATE CE 2003

A reinforced concrete beam, size $$200$$ $$mm$$ wide and $$300$$ $$mm$$ deep overall is simply supported over a span of $$3$$ $$m.$$ It is subjected to two point loads $$P$$ of equal magnitude placed at middle third points. The two loads are gradually increased simultaneously. Beam is reinforced with $$2$$ $$HYSD$$ $$415$$ bars of $$16$$ $$mm$$ diameter placed at an effective cover of $$40$$ $$mm$$ on bottom face and nominal shear reinforcement. The characteristic compressive strength and the bending tensile strength of the concrete are $$20.0\,\,N/m{m^2}$$ and $$2.2\,\,N/m{m^2}$$ respectively.

Ignoring the presence of tension reinforcement, the value of load $$P$$ in $$kN$$ when the first flexure crack will develop in the beam is

GATE CE 2003

The theoretical failure load of the beam for attainment of limit state of collapse in flexure is

GATE CE 2003

Read the following two statements

$${\rm I}.\,\,\,\,\,\,\,\,\,\,\,\,$$ Maximum strain in concrete at the outermost compression fibre is taken to be $$0.0035$$ in bending
$${\rm II}.\,\,\,\,\,\,\,\,\,\,\,\,$$ The maximum compressive strain in concrete in axial compression is taken as $$0.002$$ Keeping the provisions of $$IS$$ $$456$$-$$2000$$ on limit state design in mind, which of the following is true?

GATE CE 2002

As per provision of $$IS$$ $$456$$-$$2000$$, in the limit state method for design of beams, the limiting value of the depth of neutral axis in a reinforced concrete beam of effective depth $$'d'$$ is given as

GATE CE 2002

Identify the FALSE statement from the following, pertaining to the design of concrete structures.

GATE CE 2001

The following two statements are made with reference to a simply supported under - reinforced $$RCC$$ beam:

$${\rm I}.\,\,\,\,\,\,\,\,\,\,\,\,$$ Failure takes place by crushing of concrete before the steel has yielded.
$${\rm II}.\,\,\,\,\,\,\,\,\,\,$$ The neutral axis moves up as the load is increased.

With reference to the above statements, which of the following applies?

GATE CE 2000

Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as $$1.0.$$

A rectangular under-reinforced concrete section of $$300$$ $$mm$$ width and $$500$$ $$mm$$ effective depth is reinforced with $$3$$ bars of grade $$Fe$$-$$415,$$ each of $$16$$ $$mm$$ diameter. Concrete mix is $$M20.$$

The depth of the neutral axis from the compression fibre is

GATE CE 2000

Assume straight line instead of parabola for stress-strain curve of concrete as given below and partial factor of safety as $$1.0.$$

The depth of the neutral axis obtained as per $$IS:$$ $$456$$-$$2000$$ differs from the depth of neutral axis obtained in $$Q.08$$ by

GATE CE 2000