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The correct choice is (d) point load should be applied within a distance d from adjacent opening

Explanation: General guidelines for design of beams with openings are as follows : (i) The diameter of circular opening should be RESTRICTED to 0.5D, where D is DEPTH of beam, (ii) For RECTANGULAR unstiffened openings, depth should be less than 0.5D and LENGTH less than 1.5D, where D is depth of beam (III) For rectangular stiffened openings, depth should be less than 0.7D and length less 2D, where D is depth of beam (iv) Point loads should not be applied within a distance d from the adjacent opening.

Correct ANSWER is (a) web opening should be AWAY from support by twice the beam depth

To elaborate: General guidelines for design of beams with openings are as follows : (i)The hole should be centrally placed in web and eccentricity should be avoided, (ii) The best location for the opening is within the middle one third of the SPAN, (III) Web opening should be away from support and it should be away by twice the depth of beam, (iv) CLEAR spacing between openings should be more than depth of beam.

The correct OPTION is (d) root of fillet

Best explanation: The most critical LOCATION for failure due to WEB CRIPPLING is root of fillet since resisting area has the SMALLEST value here.

Correct choice is (a) web crippling is buckling of web caused by compressive force DELIVERED through flange

To explain: Web crippling is buckling of web caused by compressive force delivered through flange. To keep BEARING stresses within permissible limits, the concentrated load should be TRANSFERRED from FLANGES to web on sufficiently large bearing areas.

The CORRECT choice is (c) d

To EXPLAIN: Bottom flange is assumed to be restrained against lateral deflection and ROTATION. for top flanges, the end RESTRAINTS and effective DEPTH of the web are to be considered. The effective depth when top flanges are restrained against rotation but not against lateral deflection is d, where d is depth of web.

Correct choice is (a) λLT = √(βbZpfy/Mcr)

To explain: Non-dimensional SLENDERNESS RATIO is GIVEN by λLT = √(βbZpfy/Mcr), where βb= 1 for plastic and compact sections, βb= Ze/ZP for semi-compact sections, Ze = elastic section modulus, Zp = plastic section modulus, Mcris elastic CRITICAL moment.

The CORRECT choice is (c) (2[Vd/V] -1)^2

To ELABORATE: The value of β in equation of moment capacity of plastic SECTION for V > 0.6Vd is given by β = (2[Vd/V] -1)^2, where Vd =design SHEAR strength as governed by web yielding or web buckling, V = factored applied shear force.

Correct answer is (a) bi ≤ L0 / 10

For explanation: As per IS 800:2007, SHEAR lag effects in flanges may be DISREGARDED for internal elements if bi ≤ L0 / 10, where bi = width of internal element, L0 = LENGTH between points of zero moment in the span.

The correct answer is (d) the phenomenon of non uniform bending stress DUE to influence of shear strain induced on bending stresses in flanges

The best explanation: The shear strain induced INFLUENCES bending stresses in flanges and causes sections to warp. This consequently modifies the bending stresses DETERMINED by simple bending theory and RESULTS in higher stresses near junction of web to flange elements with stress dropping as DISTANCE from beam web increases. The resultant stress distribution across flange is therefore non uniform and this phenomenon is known as shear lag.

The correct option is (d) MD = Zefy/γm0

The explanation: Few I-and channel sections are semi-compact because of width-thickness RATIO. The moment capacity of semi-compact section for V > 0.6Vd is given by Md = Zefy/γm0, where Ze = ELASTIC section modulus of whole section, fy = YIELD stress of material, γm0 = partial safety factor.

Correct answer is (C) 0.9fuAnf/γm1 ≥ fyAgf/γm0

Easiest explanation: IS 800 permits bolt holes in the flanges to be ignored when the tensile fracture strength of flange is at least equal to tensile yield strength i.e. when 0.9fuAnf/γm1 ≥ fyAgf/γm0or (Anf/Agf) ≥ (fy/fu)x(γm1 /γm0)x(1/0.9), where Anf/Agf = RATIO of net AREA to GROSS area of tension flange, fy/fu= ratio of yield stress to ultimate stress of material, γm1 /γm0= ratio of PARTIAL safety factors against ultimate stress to yield stress.

Correct choice is (a) Md = Zefy‘

To explain: The DESIGN BENDING strength for slender sections is GIVEN by Md = Zefy‘ , where Ze is elastic section modulus of cross section and FY‘ is reduced design strength for slender sections.

Correct choice is (b) Md ≤ 1.5Zpfy/γm0

For EXPLANATION I would say: The CHECK for design BENDING strength for cantilever beams is given by Md ≤ 1.5Zpfy/γm0 to ensure that onset of plasticity under unfactored loads – DEAD loads, imposed loads and wind load- is prevented.

Correct OPTION is (c) Md ≤ 1.2Zpfy/γm0

For explanation: The check for design bending strength for simply supported BEAMS is given by Md ≤ 1.2Zpfy/γm0 to ENSURE that onset of plasticity under unfactored LOADS is PREVENTED.

Right answer is (a) web area is ineffective

For explanation: When shear EXCEED the limit V&gt0.6Vd, web area will be ineffective and only flanges will RESIST the MOMENT. Because of this for HIGH shear case, moment capacity of beam is reduced.

The correct answer is (c) ≤ 0.6Vd

The explanation is: When shear force V ≤ 0.6Vd, the WEB area will be FULLY effective and entire CROSS section of beam will be effective in RESISTING the MOMENT.

Correct answer is (b) VN/γm0

Easy EXPLANATION: The design shear strength is GIVEN by Vd = Vn/γm0 , where Vn= plastic shear RESISTANCE, γm0= partial factor of safety.

The correct ANSWER is (C) shear area x fy/√3

The EXPLANATION is: Plastic shear resistance is given by Vp = shear area x fy/√3.

Right option is (d) yield STRESS

Easy EXPLANATION: The DESIGN bending STRENGTH of laterally SUPPORTED beams is governed by yield stress and that of laterally unsupported beams is governed by lateral torsional buckling.

The correct CHOICE is (a) MCR < My

Easy explanation: If Mcr CRITICAL moment of a section is LESS than yield moment My , then BEAM buckles elastically.

The CORRECT choice is (d) stresses developed during manufacturing

Explanation: During the PROCESS of MANUFACTURE,steel sections are subjected to LARGE thermal expansions resulting in yield level strains in sections. As subsequent cooling is not uniform throughout the section, self-equilibrating patterns of stresses are formed. These stresses are called RESIDUAL stresses.

Correct choice is (c) both arrangement and level of application of load

To explain: The lateral stability of tranversely loaded BEAM is DEPENDENT on the arrangementof load as well as level of application of loads with respect to centroid of CROSS section.

Correct choice is (B) POINT load ACTING at tip

To EXPLAIN: For cantilevers, the most severe loading condition is point load acting at the tip because the tip is UNSUPPORTED.

Correct answer is (a) INCREASES

Explanation: Provision of INTERMEDIATE LATERAL SUPPORTS increases the lateral stability of beam. For bracings to be effective, the braces should be prevented from moving in AXIAL direction.

The correct option is (b) CLOSED section has high torsional stiffness

To elaborate: I-section with the LARGER in-plane bending stiffness does not have matching stability. in contrast, closed sections such as TUBES, boxes and solid shafts have high torsional stiffness, often high as 100 TIMES that of an open section.

Right ANSWER is (C) long shallow girders have LOW warping stiffness

For explanation I would say: Short and DEEP girders have very high warping stiffness while long shallow girders have low warping stiffness or RESISTANCE.

Correct CHOICE is (c) shape and MATERIAL of beam

The best I can explain: √EIyGItdepends on shape and material of beam, where = flexural RIGIDITY(minor axis), GIt = TORSIONAL rigidity.

Right choice is (c) MOMENT of inertia about bending axis is EQUAL to or LESS than moment of inertia out of plane

For EXPLANATION: It is not POSSIBLE for lateral torsional buckling to occur if moment of inertia of sectionabout bending axis is equal to or less than moment of inertia out of plane.

Correct answer is (a) (π/L){√[(EIyGIt) + (πE/L)^2IwIy]}

To elaborate: ELASTIC critical moment is given by MCR = (π/L){√[(EIyGIt) + (πE/L)2IwIy]}, where EIY = flexural rigidity(minor axis), GIt = torsional rigidity, It= St.Venant torsion constant, Iw = St.Venant warping constant, L = unbraced length of beam subjected to constant moment in PLANE of web.

Right option is (d) pure torsional RESISTANCE and warping torsional resistance

Explanation: Critical bending MOMENT CAPACITY of a beam UNDERGOING lateral torsional buckling is a function of pure torsional resistance and warping torsional resistance.

The correct answer is (a) SECTION POSSESSES different STIFFNESS in two principal PLANES

Explanation: Lateral instabilities occurs only if following conditions are SATISFIED : (i) section possesses different stiffness in two principal planes, (ii) applied loading induces bending in stiffer plane (about major axis).

The correct option is (b) bending MOMENT at which beam fails by lateral BUCKLING

Easiest explanation: Bending moment at which beam fails by lateral buckling when SUBJECTED to a uniform end moment is CALLED elastic critical moment.

Right choice is (b) entire CROSS section ROTATES as rigid disc without any cross sectional distortion

Explanation: The characteristic feature if LATERAL buckling is entire cross section rotates as rigid disc without any cross sectional distortion. This behaviour is similar to axially compresses long column which after initial shortening in axial direction, deflects LATERALLY when it buckles.

The correct option is (d) three DIMENSIONAL

For EXPLANATION I WOULD say: Lateral buckling in BEAM is three dimensional in nature. It involves coupled lateral deflection and twists that is when beam deflects laterally, the applied moment exerts a torque about the deflected longitudinal axis, which causes the beam to twist.

The correct option is (a) adequate restraints are PROVIDED to BEAM

Explanation: In laterally restrained beams, adequate restraints are provided to beam in plane of COMPRESSION flange.

Correct choice is (C) moment of INERTIA about principal axis normal to the web is considerable larger than moment of inertia about principal axis PARALLEL to the web

Explanation: In beam design, sections are PROPORTIONED as such that moment of inertia about principal axis normal to the web is considerable larger than moment of inertia about principal axis parallel to the web to achieve economy. Such sections are relatively weak in BENDING resistance.

Right option is (d) compression flange of BEAM is not restrained from moving laterally

To elaborate: Two IMPORTANT ASSUMPTIONS are made to achieve ideal beam behaviour: (i) compression flange of beam is restrained from moving laterally, (ii) any form of LOCAL buckling is prevented. A beam loaded predominantly in flexure would attain its full moment capacity if local and lateral INSTABILITIES of beam are prevented.

The correct OPTION is (a) for optimum bending resistance, beam material should be near neutral axis

Best explanation: For optimum bending resistance, beam material should be far away from neutral axis and web area of beam has to be adequate for resisting shear. Maximum bending and maximum shear usually occur at different cross section. in continuous beams, they MAY occur at same cross section near interior supports, but interaction effects are NORMALLY NEGLECTED.

The correct option is (b) at LEAST symmetrical about one of the PRINCIPAL axes

To elaborate: The BEAM SECTIONS should be at least symmetrical about one of the principal axes as per IS SPECIFICATION. Angle and T-sections are inherently weak in bending while channels can only be used for light loads. Rolled I0section is generally preferred as beam.