Determine the axial strength of the plates in direct tension, Civil Engineering

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The two plates shown below are each 10-in. wide by ¾- in. thick. The gage distance, g, and the longitudinal spacing on each member is set at 4-in. Determine the axial strength of the plates in direct tension. Assume grade 36 steel (Fy = 36 ksi, Fu = 58 ksi). The bolts used are ¾-in.

637_Determine the axial strength of the plates in direct tension.png

A) 322 kip

B) 273 kip

C) 416 kip

D) 243 kip

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6/1/2013 2:23:01 AM Answer: Gross Yielding: φTn= 0.9036 ksi 10-in. * 0.75-in. = 243 kip Net fracture: There are three possible failure modes for the net section: For failure mode 1, the net section is: A_n = (10-in. - 2(13/16-in.))0.75-in = 6.28 in² For failure mode 2 and 3, the net section is: A_n = (10-in. - 3(13/16-in.)+2((4-in)²/(44-in.))0.75-in = 9.5625 in² The smallest area will govern, so failure mode 1 will be the lowest: φTn = 0.7558 ksi 6.28in2 = 273 kip Thus, the gross section is lower, the answer is 243 kips.

6/1/2013 2:23:01 AM

Answer:

Gross Yielding:

φTn= 0.90*36 ksi * 10-in. * 0.75-in. = 243 kip

Net fracture:

There are three possible failure modes for the net section:

For failure mode 1, the net section is:

A_n = (10-in. - 2*(13/16-in.))*0.75-in = 6.28 in²

For failure mode 2 and 3, the net section is:

A_n = (10-in. - 3*(13/16-in.)+2*((4-in)²/(4*4-in.))*0.75-in = 9.5625 in²

The smallest area will govern, so failure mode 1 will be the lowest:

φTn = 0.75*58 ksi * 6.28in2 = 273 kip

Thus, the gross section is lower, the answer is 243 kips.

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