Explanation Given information: A W 14X 26 composite beam, thickness, t = 4.5 inches, effective slab width = 66 inches, span length, L = 30feet. The value of f c ' = 4 k s i . Calculation: We have to check whether the studs satisfy the ASIC specifications. From AISC specifications the maximum stud diameter will be equal to d maximum = 2.5 t f Where, d maximum is the maximum diameter and t f is the flange thickness. Substitute the values in the equation, we get: d maximum = 2.5 × 0.525 d maximum = 1. 3125 in . Comparing the diameter of the stud and maximum diameter, we have: Maximum diameter is d maximum = 1. 3125 in and stud diameter is d = 0.75 in 1. 3125 in > 0.75 in d maximum > d From the formed steel deck, the maximum diameter according to the AISC specifications, we have: d maximum formed = 0.75 i n Comparing the diameter of the stud and maximum diameter for formed steel deck, we have 0.75 i n = 0.75 i n d = d maximum formed Therefore, 3 4 i n × 3 i n stud is a satisfactory stud element. The area of stud using the following equation as follows: A s t u d = π 4 d 2 Where, the diameter of the stud is d. Substitute 3 4 i n for d: A s t u d = π 4 [ 3 4 ] 2 i n 2 A s t u d = 0.4417 i n 2 We have the modulus of elasticity of concrete as follows: E C = ( w C ) 3 2 f C ' k s i Where, the modulus of elasticity of concrete is E C , unit weight of concrete is w C and the 28-day compressive strength of concrete is f C ' . Substitute 145 l b f t 3 for w C and 4 k s i for f C ' . E C = ( 145 l b f t 3 ) 3 2 4 k s i E C = 1746.03 l b f t 3 × 2 k s i E C = 3492.06 k s i . Calculating the shear strength of stud with the following formula: Q n = 0.5 A s t u d f C ' E C Substitute the values, we get: Q n = 0.5 × 0.4418 4 k s i × 3492 k s i Q n = 26.11 k i p s Calculate the spacing of studs using the following equation. S = L N Where, S is the spacing. Substitute the values, we have: S = L N S = 40 × 12 34 S = 14.12 i n . Implying that one stud at each location is satisfactory. Now, the upper limit of the shear strength is as follows: Q n n = R g R p A s t u d F u Q n n = 1 × 0.6 × 0.4417 i n 2 × 65 k s i Q n n = 17.23 k i p s . As, the calculated value is less than the upper limit given by AISC, take the shear strength as: Q n n = 17.23 k i p s . The number of studs required for the half beam are as follows: N ' = N 2 Where, S is the spacing. Substitute the values, we have: : N ' = N 2 N ' = 34 2 N ' = 17. Now, the compressive force of the beam will be selected in such a way that the smallest of the compressive force in steel, compressive force of concrete slab and combined shear strength of studs. Calculate the compressive force below: C = min ( C C , C S , ∑ Q n ) Where, the compressive force is C, the compressive force of concrete is C C , and the compressive force of steel beam is C S . Calculate the compressive force in steel as follows: C S = A S F Y Where, the area of steel section is A S and the yield strength of steel is F Y . Get the value of A S from properties and dimensions table from part 1 of the manual. A S = 11.8 i n c h e s 2 . C S = 11.8 i n c h e s 2 × 50 K s i C S = 590 K i p s . We have the effective flange width of the following section as follows: b = min of [ 12L AB t inches , 12L p inches ] b = min of [ 12×40 4 inches, 12×10 inches ] b = min of [ 120 inches, 120 inches ] b = 120 inches . Calculate the compressive force in concrete below: C C = 0.85 f C ' b ( t − c ) Where, b is the width of the concrete slab, t is the thickness of the concrete beam, c is the thickness of the steel deck and f C ' is the compressive strength of the concrete. C C = 0.85 f C ' b ( t − c ) C C = 0.85 × 4 k s i × 120 i n × ( 4.5 − 1.5 ) i n C C = 0.85 × 4 k s i × 120 i n × ( 3 ) i n C C = 1224 k i p s Compute the shear strength of the studs using the equation. ∑ Q n = Q n × N ' Where, ∑ Q n is the combined shear strength of the studs. ∑ Q n = Q n × N ' ∑ Q n = 17.23 × 17 kips . ∑ Q n = 292.91 kips . Therefore, the compressive force is as follows: C = min ( C C , C S , Q n ) C = min ( 1224 k i p s , 590 k i p s , 292.91 k i p s ) C = 292.91 k i p s . The plastic neutral axis is determined by compressive strength of concrete as it lies in the steel beam. The distance of the plastic neutral axis from the top of the steel beam by equating the compressive force and tensile force as given below: C + C S − T = 0 Rearranging the equation as follows: C + F y b f t ' − F y ( A s t u d − b f t ' ) = 0 Substituting the required values, we get: C + F y b f t ' − F y ( A s t u d − b f t ' ) = 0 292.91 + 50 K s i × 6.02 i n × t ' − 50 K s i ( 11.8 i n 2 − 6.02 i n × t ' ) = 0 292.91 + 301 t ' − 590 K i p s + 301 t ' = 0 602 t ' − 297.09 K i p s = 0 503 t ' = 297.09 K i p s t ' = 297.09 503 t ' = 0.5906 t ' = 0.591 i n . Now, the compressive strength Imparted by the steel beam using the equation as follows. : C S = F y b f t ' Where, C S is the compressive strength imparted by the steel beam. Substituting the values, we get: C S = F y b f t ' C S = 50 K s i × 6

Steel Design (Activate Learning with these NEW titles from Engineering!)

6th Edition

ISBN: 9781337094740

Author: Segui, William T.

Publisher: Cengage Learning

See similar textbooks

Concept explainers

Composite Construction

Composite construction is the construction of structures in which two or more materials are used. Regarding structural engineering, composite construction is a construction where two materials are bound together in a technical manner such that both the m…

Question

Chapter 9, Problem 9.7.4P

To determine

The adequate strength of the composite section by LFRD method.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9, Problem 9.7.3P

Chapter 9, Problem 9.8.1P

Students have asked these similar questions

Given a circular curve connecting 2 tangents that intersect at an angle of 55°. The PI is at thestation (948+50) and the design speed of the highway is 70 mi/h. Determine:(a) stations of the PC and PT(c) Deflection angles and chord lengths for the first, middle, and last chords

A simple circular curve exists with a radius of 900 ft connects the tangents of a two-lanehighway that has a posted speed limit of 45 mph. The highway curve is not superelevated,e=0. A structure is proposed on land on the inside of the curve. Assume the road is on a levelgrade. Determine the minimum distance allowable between the proposed structure and thecenterline of the curve such that the current maximum safe speed of the curve would notneed to be reduced

A +4.4% grade intersects with a -3.3% grade at a station (550+30) at an elevation of400 ft. If the design speed is 60 mi/h, determine:(a) the minimum length of the vertical curve using the rate of vertical curvature(b) the stations and elevations of the BVC and EVC(c) the tangent and curve elevations of BVC, full stations, and EVC(d) the station and elevation of the highest point

Chapter 9 Solutions

Steel Design (Activate Learning with these NEW titles from Engineering!)

Ch. 9 - Prob. 9.1.1P Ch. 9 - Prob. 9.1.2P Ch. 9 - Prob. 9.1.3P Ch. 9 - Prob. 9.1.4P Ch. 9 - Prob. 9.1.5P Ch. 9 - Prob. 9.1.6P Ch. 9 - A W1422 acts compositely with a 4-inch-thick floor...Ch. 9 - Prob. 9.2.2P Ch. 9 - Prob. 9.3.1P Ch. 9 - Prob. 9.3.2P

Ch. 9 - Prob. 9.4.1P Ch. 9 - Prob. 9.4.2P Ch. 9 - Prob. 9.4.3P Ch. 9 - Prob. 9.4.4P Ch. 9 - Prob. 9.4.5P Ch. 9 - Prob. 9.5.1P Ch. 9 - Prob. 9.5.2P Ch. 9 - Prob. 9.5.3P Ch. 9 - Note For Problems 9.6-1 through 9.6-5, use the...Ch. 9 - Note For Problems 9.6-1 through 9.6-5, use the...Ch. 9 - Note For Problems 9.6-1 through 9.6-5, use the...Ch. 9 - Note For Problems 9.6-1 through 9.6-5, use the...Ch. 9 - Note For Problems 9.6-1 through 9.6-5, use the...Ch. 9 - Prob. 9.7.1P Ch. 9 - Prob. 9.7.2P Ch. 9 - Prob. 9.7.3P Ch. 9 - Prob. 9.7.4P Ch. 9 - Prob. 9.8.1P Ch. 9 - Prob. 9.8.2P Ch. 9 - A beam must be designed to the following...Ch. 9 - Prob. 9.8.4P Ch. 9 - Prob. 9.8.5P Ch. 9 - Prob. 9.8.6P Ch. 9 - Prob. 9.8.7P Ch. 9 - Prob. 9.8.8P Ch. 9 - Use the composite beam tables and select a W-shape...Ch. 9 - Prob. 9.8.10P Ch. 9 - Prob. 9.10.1P Ch. 9 - Prob. 9.10.2P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.