Beams MCQ Quiz - Objective Question with Answer for Beams - Download Free PDF

Explanation:

As per IS 800: 2007 (General Construction in Steel — Code of Practice):

• Lateral Torsional Buckling (LTB) is a stability concern primarily for open sections (like I-beams) when bending about their major axis and the compression flange is unrestrained.

• Hollow rectangular or tubular sections are closed shapes and geometrically stable in torsion.

• Their symmetry and enclosed shape resist both lateral displacement and twisting, making LTB checks generally unnecessary.

Additional Information

• Plate girders: Require LTB checks, especially due to their large depth and slenderness.
• Beams bending about their major axis with λLT more than 0.4: Higher slenderness ratio indicates potential for buckling; LTB check is required.
• I-section beams with a long span: More susceptible to LTB due to unrestrained compression flange over long lengths.

Explanation:

• When a beam is not laterally supported, it is susceptible to lateral-torsional buckling (LTB).

• Lateral torsional buckling occurs when a beam under bending experiences out-of-plane deformation, causing it to twist and bend laterally.

• This phenomenon reduces the design bending strength and is governed by lateral torsional buckling strength.

Additional Information

1. Yield stress 

   • Yield stress is a material property but does not govern bending strength due to lateral instability.

2. Shear buckling strength 

   • Shear buckling governs web buckling in thin-walled sections but does not control lateral buckling.

3. Flexural buckling strength 

   • Flexural buckling applies to axial compression members (columns), not bending members.

Lateral torsional buckling (LTB) occurs when a beam under bending about its strong axis deflects laterally and twists. For LTB to be analyzed accurately, it is crucial to assume certain conditions. If the beam has no initial imperfections and behaves elastically, it simplifies the analysis because the material properties are consistent and predictable under loading. When loaded by unequal and opposite end moments in the plane of the web, the beam experiences a bending moment causing potential buckling. Residual stresses and boundary conditions like simply supported ends influence the critical buckling moment. Simplified conditions help in understanding and predicting LTB behavior more effectively.

List I (Sections)		List II (Limiting width to thickness ratio)
P.	Rolled section	3.	15.7ε
Q.	Welded section	4.	13.6ε
R.	Circular hollow section	1.	88ε2
S.	Hot rolled RHS	2.	42ε

Modes of Local Failures in Steel Beams:

• Buckling of Thin Flanges of Section: This occurs when the thin flanges of the beam section are subjected to compressive forces, causing them to buckle. This type of failure is common in beams with slender and thin flanges.
• Local Crushing of Web: Local crushing happens when the web of the beam experiences high localized compressive stresses, leading to failure by crushing. This typically occurs near concentrated loads or support points where the stress is highest.
• Shear Yield of Web: Shear yield refers to the yielding of the web due to high shear forces. This kind of failure is characterized by the web material yielding in shear, which can lead to large deformations and eventual failure of the beam.

Incorrect Mode of Local Failure:

• Torsional Buckling: Torsional buckling is not considered a mode of local failure in steel beams. Instead, it is a global instability phenomenon where the beam twists and buckles about its longitudinal axis. This type of failure is more related to the overall stability of the beam rather than local failure mechanisms.

Buckling strength:

A certain portion of the beam at supports acts as a column to transfer the load from the beam to the support. Hence, under this compressive force, the web may buckle. This may happen under a concentrated load on the beam also. The load dispersion angle is taken as 45° with the horizontal.

Bearing area is calculated at the root of the web by dispersion at a slope of 1:2.5.

∴ The angle dispersion of a concentration load on the flange to the web plate of a steel beam is 45° with the horizontal.

Explanation:

As per IS 800: 2007, CL: 5.2.2.2, Limit state of serviceability includes the following:

1. Crack due to fatigue

2. Repairable damage

3. Corrosion

4. Fire

5. Deformation and Deflections

6. Vibrations in structure

Hence, ’fracture due to fatigue’ cannot be considered as limit state of serviceability of a steel structure as it is considered in Limit State of Strength.

Additional Information

Limit State of Collapse includes the following:

1. Fracture due to fatigue.

2. Brittle fracture.

3. Loss of Equilibrium of structure.

4. Loss of stability of structure.

Explanation:

As per IS 800:2007 , clause number 5.6.1, page number 31, table number 6,

For an industrial buildings ,

Purlins and Girts , deflection for elastic cladding = span/150 ;

defelction for brittle cladding = span/180;

Permissible maximum vertical deflection= \( {span \over 150}\) = 3600/150 = 24mm

Explanation: 

The design bending strength of a laterally supported beam is given by:

 \(M_{d}=\frac{\ _{\beta _{b}Z_{p}f_{y}}}{\gamma _{mo}}\)

Where

 \(\beta\)_b= 1.0 for plastic and compact section

\(Z\)_p= Plastic section modulus of cross section

\(f\)_y= Yield stress of material

\(\gamma\)_mo= 1.1 (partial safety factor. 

According to IS 800, clause no. 8.7.1.5,

The buckling resistance should be based on the design compressive stress of a strut, the radius of gyration being taken about the axis parallel to the web. The effective section is the full area or core area of the stiffener together with an effective length of web on each side of the centreline of the stiffeners, limited to 20 times the web thickness. The design strength used should be the minimum value obtained for buckling about the web or the stiffener.

Spandrel beam:

• Supporting load from exterior wall and slab and spanning from column to column.
• In the case of high rise buildings, the masonry walls are usually not able to withstand their self-weight and the slab weight. In such cases, the beams are provided with exterior walls at each floor level to support the wall load and perhaps some roof load also. These beams are termed as spandrels.

Stringer beams:

• These are secondary beams (typically used in truss bridges) to carry the load from the slab till the cross beams located at truss nodes. You can see them in roof systems supported by trusses too. Basically, their purpose is to convert distributed loads to point loads (at truss nodes).

Explanation:

(i) Purlins are designed as continuous beams because they span over more than two truss joint and are supported by rafters.

(ii) Principal rafter is the top chord member of truss and is subjected to compressive forces from loads transferred by purlins at the nodes.

(iii) The rafters act as simply supported beams between the purlins.

(iv) The purlins are interconnected by sag rod or tie rod at the centre span of purlin to reduce bending moment and deflection in the purlin.

Concepts:

.As per IS 800:1987,

Maximum permissible direct tensile stress in structural steel is 0.60 fy

Maximum permissible direct compressive stress in structural steel is 0.60 fy

Maximum permissible bending tensile stress in structural steel is 0.66 fy

Maximum permissible bending compressive stress in structural steel is 0.66 fy

Maximum permissible average shear stress in structural steel is 0.40 fy

Maximum permissible bearing stress in structural steel is 0.75 fy

Calculation:

Given: f_y = 250 MPa

τ = 0.4 × 250 = 100 N/mm²

Additional Information The nominal shear yielding strength of webs is based on the Von –Misses yield criterian, which states that for an un-reinforced or unstiffened web of a beam, whose width to thickness ratio is comparatively small so that web buckling is avoided , the shear strength is  given as

 τ = 0.58 fy

However, IS 800 adopted shear strength as:

τ = 0.6 × fy

where fy­ is the yield strength of material

The above relation is only hold when there is no shear buckling of web and this is only possible when depth to thickness ratio of web is very small

To ensure that the compression flange of the beam is restrained from moving laterally, the cross-section must be plastic or compact. If significant ductility is required, the section must invariably be plastic.

The different types of the section are as follows:

1. Plastic - Cross-sections, which can develop plastic hinges and have, the rotation capacity required for the failure of the structure by formation of a plastic mechanism, are called plastic sections. The stress distribution for these sections is rectangular.

2. Compact - Cross-sections, which can develop the plastic moment of resistance, but have inadequate plastic hinge rotation capacity for the formation of a plastic mechanism before buckling classed as compact sections. These cross-sections may develop fully plastic stress distribution across the entire cross-section but do not have adequate ductility. The stress distributions for these sections are rectangular.

3. Semi-compact– Cross sections, in which the extreme fiber in compression can reach yield stress but cannot develop the plastic moment of resistance due to local buckling are called semi-compact or non-compact sections. These sections are used in the elastic design and the stress distribution for such sections is triangular.

4. Slender – Cross sections in which the elements buckle locally even before the attainment of yield stress are classed as slender sections.

The cross-section which may develop plastic stress distribution fully but does not have adequate ductility is classified as a compact section.

Explanation:

A beam having the flange and the web is mainly I beams or H beams in which the horizontal elements are called flanges and vertical elements on the web. These are usually made of structural steel and are used in construction and civil engineering work.

Let us consider an I section like the example of a rolled steel section.

Shear stress distribution in I-section-