Plate Girder MCQ Quiz - Objective Question with Answer for Plate Girder - Download Free PDF

Transverse Stiffeners are provided to increase buckling resistance of the web due to inclined compressive stress due to shear, It is provided vertically along the span.

Horizontal Stiffener / Longitudinal Stiffener is designed to prevent web buckling due to bending compression.

Both traverse and longitudinal stiffeners are provided to check the web buckling.

End Bearing Stiffeners are provided at the supports & Load Bearing Stiffeners are provided at the points of concentrated loads.

Important Point:

if \(\frac{d}{{{t_W}}}\)< 67ϵ ⇒ unstiffened girder can be designed i.e. No girder required.

If 85 ϵ < \(\frac{d}{{{t_W}}}\)< 200 ϵ ⇒ Vertical stiffener (C1 and C2) may be provided.

If 200 ϵ < \(\frac{d}{{{t_W}}}\) < 250 ϵ ⇒ Vertical stiffener along with longitudinal stiffener at 0.2 d may be provided.

If 250 ϵ < \(\frac{d}{{{t_W}}}\) < 345 ϵ ⇒ Vertical stiffeners along with two longitudinal stiffeners at 0.2 d and 0.5 d respectively may be provided.

Explanation:

• Intermediate transverse stiffeners or vertical stiffeners are provided to stiffen the web and prevent shear buckling.
• Longitudinal stiffeners or horizontal stiffeners are used to increase buckling resistance under bending.

Explanation:

Functions of Various Elements of a plate girder:

1. Flanges:

(i) Flanges of required width and thickness are required to resist the flexural moment due to dead and superimposed load coming on the plate girder bt developing compressive force in one flange and tensile in the other flange i.e. by developing resisting couple.

2. Web:

(i) Web of required depth and thickness is required to keep the flange plates at the requisite distances and to resist shear in the beam.

3. Stiffeners:

(i) Stiffeners are provided to safeguard the web against local buckling failure.

(ii) These stiffeners are provided either in the longitudinal direction called as Horizontal stiffeners or in the traverse direction called as vertical stiffeners or in both directions.

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Stiffeners and their purposes are furnished below.

Explanation:

DESIGN OF WEB PLATE

The web of a plate girder is primarily designed to resist shear force. The design of web plate consists of determination of:
(i) depth (d) of web plate, and
(ii) thickness (t_w) of the web plate.

The economical depth of the web plate is given by the equation:

\( d = 1.1 \sqrt{\frac{M}{\sigma_{bc} \cdot t_w}} \)

Alternatively, as per Rawter and Ciark (in their book Elementary Theory and Design of Flexural Members), the economical depth is:

\( d = k \left( \frac{M}{\sigma_{bc}} \right)^{1/3} \)  

Where:

• M = Maximum bending moment in N·mm
• σ_bc = Permissible bending stress in compression (N/mm²)
• k = Constant, taken as:
  • 5 for welded plate girder
  • 4.5 for riveted girder with stiffeners

Explanation:

Statement 1 (S1):  Correct

"Longitudinal stiffeners increase the buckling resistance considerably when the web is subjected to buckling."

• Longitudinal stiffeners are provided parallel to the flange and effectively increase the buckling resistance of the web.

• These stiffeners help in distributing the load and resisting shear buckling.

• Since this statement is correct, it is not an incorrect statement.

Statement 2 (S2):  Correct

"Bearing stiffeners are used to transfer concentrated loads on the girder and heavy reactions at supports to the full depth of the web."

• Bearing stiffeners are vertical stiffeners provided at points of concentrated loads or support reactions.

• They prevent local buckling of the web and ensure load transfer over the full depth.

• Since this statement is correct, it is not an incorrect statement.

Statement 3 (S3):  Incorrect

"Bearing stiffeners are called stability stiffeners."

• Bearing stiffeners are provided to resist local buckling due to concentrated loads but are not classified as stability stiffeners.

• Stability stiffeners are different from bearing stiffeners and are primarily used to enhance the overall stability of the web against lateral buckling.

• Since this statement is incorrect, it is the wrong statement.

Explanation:

Transverse Stiffeners are provided to increase buckling resistance of the web due to inclined compressive stress due to shear, It is provided vertically along the span.

Horizontal Stiffener / Longitudinal Stiffener is designed to prevent web buckling due to bending compression.

Both traverse and longitudinal stiffeners are provided to check the web buckling.

End Bearing Stiffeners are provided at the supports & Load Bearing Stiffeners are provided at the points of concentrated loads.

Important Point:

If \(\frac{d}{{{t_W}}}\)< 67ϵ ⇒ unstiffened girder can be designed i.e. No girder required.

If 85 ϵ < \(\frac{d}{{{t_W}}}\)< 200 ϵ ⇒ Vertical stiffener (C1 and C2) may be provided.

If 200 ϵ < \(\frac{d}{{{t_W}}}\) < 250 ϵ ⇒ Vertical stiffener along with longitudinal stiffener at 0.2 d may be provided.

If 250 ϵ < \(\frac{d}{{{t_W}}}\) < 345 ϵ ⇒ Vertical stiffeners along with two longitudinal stiffeners at 0.2 d and 0.5 d respectively may be provided.

If \(\frac{d}{{{t_W}}}\) ≤ 400 ϵ ⇒ End bearing stiffeners, intermediate transverse stiffeners, longitudinal stiffeners at 0.2d from compression face and at neutral axis are needed.

Explanation: 

As per IS 800:2007 In the case of plate girder with vertical stiffeners and horizontal stiffeners the lesser and greater unsupported clear dimension of web panel should not exceed 180 t and 270 t respectively. 

Important Points

• Theoretically, intermediate transverse stiffener are not required when the calculated shear stress in the web is less than the critical shear stress of the web of the plate girder since the web will not buckle and failure of web will occur due to shear yielding of the web. Here tension field will not develop and stiffener are not required and the web completely be shear resistant. 
• minimum spacing of vertical stiffener = 0.33d
• maximum spacing of vertical stiffener = 1.5d
• Lesser clear panel dimension is less than 180t_w
• Greater clear panel dimension is less than 270t_w

Explanation:

Web thickness:

(i) Initiallly the web thickness can be assumed as 6 mm (if painted) or 8 mm (if unpainted).

Minimum web thickness based on serviceability requirement:

As per CI. 8.6.1 of IS 800:2007,

(i) When transverse stiffeners are not provided and web connected to flange along both longitudinal edges,

\(\frac{d}{{{t_w}}} \le 200\ {\varepsilon _w}\)

(ii) When transverse stiffness are not provided and web connected to flanges along one longitudinal edge only

\(\frac{d}{{{t_w}}} \le 90\ {\varepsilon _w}\)

Explanation:

Economical depth of plate girder (D):

Compressive member are always based function of their depth. The depth at which the weight of girder is minimum is its economical depth.

For riveted plate girder, D = \(1.1\sqrt {\frac{{\bf{M}}}{{{{\bf{\sigma }}_{\bf{b}}}.{{\bf{t}}_{\bf{w}}}}}}\)

For welded plate girder, D = \(5.3\sqrt {\frac{{\bf{M}}}{{{{\bf{\sigma }}_{\bf{b}}}.{{\bf{t}}_{\bf{w}}}}}}\)

where M=Maximum bending moment,

\({{\rm{\sigma }}_{\rm{b}}}\) = Permissible bending stress

If the depth of girder is less than 750mm, it is called shallow plate girder.

If the depth is more than 750mm, it is called deep plate girder.

The different type of stiffeners and their function is given below in tabulated from:

Transverse Stiffeners are provided to increase buckling resistance of the web due to shear, It is provided vertically along the span.

Horizontal Stiffener / Longitudinal Stiffener is designed to prevent web buckling due to bending compression.

End Bearing Stiffeners are provided at the supports & Load Bearing Stiffeners are provided at the points of concentrated loads.

Important Point:

if \(\frac{d}{{{t_W}}}\)< 67ϵ ⇒ unstiffened girder can be designed i.e. No girder required.

If 85 ϵ < \(\frac{d}{{{t_W}}}\)< 200 ϵ ⇒ Vertical stiffener (C1 and C2 ) may be provided.

If 200 ϵ < \(\frac{d}{{{t_W}}}\) < 250 ϵ ⇒ Vertical stiffener along with longitudinal stiffener at 0.2 d may be provided.

If 250 ϵ < \(\frac{d}{{{t_W}}}\) < 345 ϵ ⇒ Vertical stiffeners along with two longitudinal stiffeners at 0.2 d and 0.5 d respectively may be provided.

Calculation:

\(\frac{d}{{{t_w}}} = \frac{{1000}}{6} = 166.67\)

As \(\frac{d}{{{t_W}}} > 85\) and \(\frac{d}{{{t_w}}} < 200\)

Therefore, intermediate vertical stiffeners are to be provided.

Concept:

Buckling

• Buckling is characterized by a sudden sideways failure of a structural member subjected to high compressive stress.
• Buckling of the web in a plate girder happens when the web is too slender to carry the transverse force being transferred from the flange.

Diagonal tension does not cause any problem but diagonal compression causes the web to buckle in the direction perpendicular to its action.

Methods to reduce Web buckling:

Reduce the depth-to-thickness ratio of the web such that problem is eliminated,

• Provide web stiffeners to form panels that would enhance the shear strength of the web.
• Provide web stiffeners to form panels that would develop tension field action to resist diagonal compression.

Important Points

• In plate girder, the flange is designed to resist bending moment
• The web is designed to resist the shear resulting from loads

Explanation:

• When web of the plate girder is not sufficient enough to carry the loads. In that case, stiffeners are provided which perform certain specific functions which are discussed below.
• In general, there are only two types of stiffener viz. intermediate stiffener and bearing stiffener but as per IS 800:2007 the following types of stiffeners are identified based on the purpose for which a stiffener is being used: 
  • Intermediate and longitudinal stiffener: To improve the buckling strength of a slender web due to shear.
  • Diagonal stiffener: Diagonal stiffener should be designed to carry a portion of applied shear and bearing that exceed the web capacity.
  • Load carrying stiffener: To prevent web buckling due to concentrated load.
  • Bearing stiffener: To prevent local crushing of the web due to concentrated loads or reaction.
  • Torsional stiffener: To provide lateral restraint to beams and girders at support.
  • Tension stiffener: To transfer tensile forces applied to the web through a flange.

Explanation: 

As per IS 800:2007 In the case of plate girder with vertical stiffeners and horizontal stiffeners the lesser and greater unsupported clear dimension of web panel should not exceed 180 t and 270 t respectively. 

Important Points

• Theoretically, intermediate transverse stiffener are not required when the calculated shear stress in the web is less than the critical shear stress of the web of the plate girder since the web will not buckle and failure of web will occur due to shear yielding of the web. Here tension field will not develop and stiffeners are not required and the web completely be shear resistant. 
• minimum spacing of vertical stiffener = 0.33d
• maximum spacing of vertical stiffener = 1.5d
• Lesser clear panel dimension is less than 180tw
• Greater clear panel dimension is less than 270tw

Explanation:

(i) The depth between the outer surfaces of the flanges is termed as overall depth or depth of the plate girder.

(ii) In general, depth of the plate girder is kept 1/10^th to 1/12^th of the span. The distance between C.G of compression flange or C.G. of tension flange is known as effective depth of plate girder.

(iii) The distance between vertical legs of flange angles at the top and at the bottom is known as clear depth of plate girder.

(iv) When the depth of plate girder is less than 750mm, then such girders are known as ‘Shallow Plate Girders’.

(v) When the depth of plate girder is more than 750mm, then such girders are known as ‘Deep Plate Girders’.