Pg 1 / 8 Badri FKM UTM BOLT nalsis and Selection (pg 396) This note is onl a guideline for using the tet book. Detailed eplaination and tables are found in Shigle Mechanical Engineering Design tet book. Objective To analze loads and stresses acting on a threaded fastener and consequentl select appropriate size of the fastener Thread Definitions -The terminolog of screw threads p d d r t l (pitch) the distance between adjacent thread forms measured parallel to the thread ais. The pitch in U.S. units is the reciprocal of the number of thread forms per inch N. The major diameter (most important reference to bolt size [eg major diameter 10mm M10] ) The minor (smallest) diameter (used in shear analsis) The tensile-stress area of the threaded part of the screw or bolt sustaining the load equal in strength to an unthreaded rod. (used in tensile stress analsis of bolts) (lead) - distance the nut moves parallel to the screw ais when the nut is given one turn. For a single thread, the lead is the same as the pitch. For double thread: l 2p and triple thread: l 3p
Pg 2 / 8 Thread Standards M10 1.5 Metric threads are specified b writing the diameter and pitch in millimeters. This thread have a nominal major diameter of 10 mm and a pitch of 1.5 mm. (Table 8-1). 0.625"-18 UNRF Unified threads are specified b stating the nominal major diameter, the number of threads per inch, and the thread series. (Table 8-2). Bolt Strength Table 8-1 (Sample) pg 398 In the specification standards for bolts, the bolt size is specified b stating the proof strength against the minimum tensile stress or von-mises stress. proof load proof strength the maimum load (force) that a bolt can withstand without acquiring a permanent set. the quotient of the proof load and the tensile-stress area. Table 8-11 (Sample) pg 420
Pg 3 / 8 FORCE ND STRESS NLYSIS The bolts are located at various location in the joint. In this analsis, the original loads applied at all the bolts are replaced b an equal load applied at the centroid plus a torque that is equal to the product of force and the distance it was moved. Based on this basic principle, centroid location must be calculated before force analsis can proceed. Calculation of CG (centroid) for a group of Bolts (or screw) 2 3 1 1 + 2 2 + 3 3 +... + n n 1 + 2 + 3 +... + n _ i 4 1 1 + 2 2 + 3 3 +... + n n 1 + 2 + 3 +... + n 1 _ 5 where is the cross-sectional area of the bolts - assuming all bolts are of the same size. Loading of Bolts There are 4 main tpes of loads acting on bolts - 2 primar and 2 secondar. Primar Load: 1. aial load per bolt, P' (or aial stress per bolt, σ' ) 2. shear load per bolt, V' (or shear stress per bolt τ' ) Secondar load: 1. bending load per bolt, P" (or bending stress per bolt, σ'' ) 2. twisting load per bolt, V" (or torsional stress per bolt τ'' )
Pg 4 / 8 Pure ial Load (P) P Tensile load per bolt : F p n ( NB : this is primar load. ) P Tensile stress per bolt : σ p total P n t n - number of bolts t - tensile stress area (see Table 8-1) Pure Shear Load, V V Shear load per bolt : S p n V Shear stress per bolt : τ p total τ p V n s if shear occurs at the shank part, then use bolt sectional-area as π d 2 s where d - major diameter 4 τ p V if shear occurs at threaded part, then use n r bolt sectional-area as r - minor diameter area (refer to Table 8-1)
Pg 5 / 8 Bending Load Moment M is force eerted on bolts b plate M P L M If force per unit distance U f n i 1 l i 2 Then force at bolt n : F n U f l n F n Secondar tensile stress : σ s t - tensile stress area (see Table 8-1) t
Pg 6 / 8 Torsional Load, T V 1 V 2 _ C V 3 T V 5 _ V 4 Twisting loads act at centroid of all bolts : T V 1 r 1 + V 2 r 2 +... + V n r n where r - distance of bolt to centroid If shear force per unit distance U n T i 1 r i 2 Then shear force at bolt n : V n Ur n V n Secondar shear stress : τ s rea could be either area s or r (If r - see Table 8-1)
Pg 7 / 8 Procedure for analsing bolt 1. 2. 3. 4. 5. 6. 7. 8. Determine the kind of loads acting on the structure Primar loads : ial load, P and/or Shear load, V Secondar loads: Bending load, M and/or Twisting load, T Draw the freebod diagram and find the location of the centroid or the pivot. Transfer all loads to the centroid/pivot. Use suitable analsis to find the most critical load. If both primar and secondar loads are shear, use summation of vector to find resultant load. If combined shear and tensile load, then calculate Von-Mises stress. If both primar and secondar loads are tensile, add both load together. Compare final stress with strength of bolt. a. Compare Von-mises stress (σ') against proof strength (S P ) b. Compare shear stresses against shear ield strength S s S (MSS) 2 Question 1 bracket (size in mm) is supported b bolts as shown in diagram below. load of F 16 kn is applied. Using bolts of Metric Class 5.8, determine the suitable bolt size for the design if η 3.0 ; Length of shank 4 mm.
Pg 8 / 8 Question 2 force F acts on a mounting bracket fied to a structure b 3 bolts as shown in diagram below. Bolt used is 1/2"-13 UNC of STM grade 307. 1. Draw the freebod diagram showing all forces acting on the bolts 2. If the force F is 2 kn, determine the status of the connection if η 3.0. 3. If the bolt is M12 1.75 of Metric Class 5.8, find the safet factor. 4. Determine the maimum load F that the bolts can carr if the bolt used are 3/4"-10 UNC of STM grade 490. Use η 2.5. (Hint: Convert metric dimensions to imperial (3 decimal points). Question 3 bracket holding a cable of tension F is shown in diagram below. It is fied to the floor b 4 bolts of STM tpe 1 grade 325. 1. Determine F, if bolt size is 3/4"-10 UNC. and given η 3 2. If tension F 50 kn and the bolts size is 1/2"-13 UNC., determine the status of the connection if recommended safet factor is 2.50 Connections Eamples Test