Structural Fasteners Practice Questions

Weld type: Circular fillet weld Effective throat thickness for fillet weld: $t = 0.7 \times 5 = 3.5 , \text{mm}$ Length of weld (perimeter of tube): $L = \pi \times 250 = 785.4 , \text{mm}$ Section modulus for circular weld (as per IS 800:2007): $Z_p = \frac{\pi \times D^2 \times t}{4}$ $Z_p = \frac{3.1416 \times 250^2 \times 3.5}{4} = 171,887.3 , \text{mm}^3$ Design shear strength of weld: $f_w = \frac{f_u}{\sqrt{3} \times \gamma_{mw}}$ For Fe410 steel, $f_u = 410 , \text{MPa}$ , shop weld $\Rightarrow \gamma_{mw} = 1.25$ $f_w = \frac{410}{\sqrt{3} \times 1.25} = 189.46 , \text{MPa}$ Torque resisted by weld: $T = f_w \times Z_p = 189.46 \times 171,887.3 = 32,545,925.8 , \text{N.mm}$ Convert to kN.m: $T = \frac{32,545,925.8}{10^6} = 32.5 , \text{kN.m}$ (Incorrect) Check formula for polar section modulus of circular weld (IS 800:2007): $Z_p = \frac{2 \pi D^2 t}{4} = \frac{\pi D^2 t}{2}$ $Z_p = \frac{3.1416 \times 250^2 \times 3.5}{2} = 343,774.6 , \text{mm}^3$ $T = 189.46 \times 343,774.6 = 65,091,851.6 , \text{N.mm} = 65.1 , \text{kN.m}$

As per IS:800-2007 Clause no. 11.2.1 Full strength of tension member,

Weld strength of $L_1$ ,

Weld strength of $L_2$ ,

Applying moment CG equal to zero,

Design capacity of welded connection $P_s=f_b \times l_{eff}\times t_t$

Shear flow in horizontal member (flange) is linear with zero at free end and in vertical member (web) it is parabolic.

Direct concentrated load (P) = 350 kN Eccentricity (e) = 100 mm Depth of weld ( $d_w$ ) at each face = 500 mm Size of weld (S) = 10 mm Throat thickness of weld ( $t_t$ ) = 0.7S = 7 mm It is a case of combined shear (P) and Bending moment (M = P.e) Shear stress acting on weld due to direct shear force P,

Bending normal stress acting at $i^{th}$ point from Neutral axis $[f_i]=\frac{M}{I}y_i$ Maximum bending stress at extreme point in weld

As per IS800:2007. Maximum resultant stress an equivalent stress in fllet weld due to combined shear and bending stress

Direct bending tensile stress, $f_{a}=150 Mpa$ Direct shear stress, $q=50 Mpa$ According to IS 800:2007, clause 10.5.10.1.1 The equivalent stress,

(Hence OK) Note: The above check for combination of stressed need not be done for fillet welds where the sum of normal and shear stresses does not exceed $f_{wd}$ [Clause 10.5.10.1.2(b)]. Thus, $f_{a}+q=150+50=200$ MPa $f_{a}+q \gt f_{wd}$ (= 184.75 MPa) $\Rightarrow \;\;f_{e}= 173.21$ MPa Thus, the weld is designed for an equivelent stress of 173.21 MPa

Factrored normal stress, $f_{a}= 120 Mpa$ factrored shear stress, $q= 50 Mpa$ According to IS-800:2007, clause 10.5.10.1.1 The equivalent stress,

Note: The above check for combination of stresses need not be done for fillet welds where the sum of normal and shear stresses does not exceed $f_{wd}$ [clause 10.5.10.1.2(b)]. Hence, sum of normal and shear stresses $=120+50=170 MPa \leq f_{wd} (= 184.75 MPa)$ So, the above check need not be done. So, weld is designed for a resultant shear stress of $\left ( f_{r} \right )$

So, the design stress is $130 N/mm^{2}$ ; however equivalent stress 147.99 MPa.

So permissible load = 60 kN

Maximum force carried by plates, $P= \frac{A_{g}f_{y}}{\gamma _{m0}}=\frac{\left ( 100\times 12 \right )\times 250}{1.1}=272.73\, kN$ Load carried by each weld $=\frac{P}{2}=136.36\, kN$ For minimum length of weld, Strength of weld = Load carried by weld $l_{W}t_{t}\frac{f_{u}}{\sqrt{3}\gamma _{mW}}= 136.36\times 10^{3}$ or, $l_{W}\times \left ( 10\times 0.7 \right )\times \frac{410}{\sqrt{3}\times 1.2}= 136.36\times 10^{3}$ $\Rightarrow l_{W}=102.9\, mm =105\, mm$ (rounded off to nearest higher multiple of 5 mm)

Tensile strength of plate in arrangement (2) will be greater than in arrangement (1), *As per IS code 800:2007 clause 6.3

Currently no explanation available

$\tan \theta =\frac{3}{4}, \; \cos \theta =\frac{4}{5}, \; \sin \theta =\frac{3}{5}$ Tension in each bolt $=\frac{4P_{u}}{5\times 6} = \frac{4\times 250}{5\times 6}=33.33 \; kN$ Shear in each bolt $=\frac{3P_{u}}{5\times 6}=\frac{3\times 250}{5\times 6}=25kN$

Clause 9.2.1 IS 800:2007

Currently no explanation available

Effective throat thickness is the shortest distance from the root of fillet weld to the face of the line joining the toes. The effective throat thickness should not be less than 3 mm. Effective throat thickness =Ks where s is the size of weld in mm and K is a constant. The value of K depends upon the angle between the fusion faces.