The beam shown in Figure P8.37 will be constructed from a standard steel W-shape using an allowable bending stress of 24 ksi. Assume PB=7.5 kips, PC=13.0 kips, PD=8.0 kips and a=5 ft. (a) Develop a list of five acceptable shapes that could be used for this beam. On this list, include the most economical W10, W12, W14, W16, and W18 shapes. (b) Select the most economical W shape for this beam. Calculate Ay and Ey, the vertical reaction forces at supports A and E, respectively. Answers: Ay = kips Ey = kips Determine the maximum bending moment magnitude for the beam. One method to obtain this value is to construct shear-force and bending-moment diagrams on a piece of paper. Determine the maximum bending moment magnitude from your bending-moment diagram. Answer: Mmax = kip-ft Calculate the minimum required section modulus if the allowable bending stress is 24 ksi. Answer: Smin = in.3 Below, fill in the missing portions of the beam shape designations for the most economical W10, W12, W14, W16, and W18 shapes that are acceptable for this case. Also, enter the corresponding section modulus for each case. Answers: The most economical W10 shape is: W10 x with S = in.3 The most economical W12 shape is: W12 x with S = in.3 The most economical W14 shape is: W14 x with S = in.3 The most economical W16 shape is: W16 x with S = in.3 The most economical W18 shape is: W18 x with S = in.3 Choose the most economical W shape for this beam. Select only from the W10, W12, W14, W16, and W18 shapes that were considered in Part 4. If you have more than one choice with the same weight, choose the shorter shape. Answer: The most economical shape has a weight of lb/ft

Structural Analysis

6th Edition

ISBN:9781337630931

Author:KASSIMALI, Aslam.

Publisher:KASSIMALI, Aslam.

Chapter2: Loads On Structures

Section: Chapter Questions

Problem 1P

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The beam shown in Figure P8.37 will be constructed from a standard steel W-shape using an allowable bending stress of 24 ksi. Assume P_B=7.5 kips, P_C=13.0 kips, P_D=8.0 kips and a=5 ft.

(a) Develop a list of five acceptable shapes that could be used for this beam. On this list, include the most economical W10, W12, W14, W16, and W18 shapes.
(b) Select the most economical W shape for this beam.
Calculate A_y and E_y, the vertical reaction forces at supports A and E, respectively.
Answers:

A_y =	kips
E_y =	kips

Determine the maximum bending moment magnitude for the beam. One method to obtain this value is to construct shear-force and bending-moment diagrams on a piece of paper. Determine the maximum bending moment magnitude from your bending-moment diagram.

Answer: M_max = kip-ft

Calculate the minimum required section modulus if the allowable bending stress is 24 ksi.
Answer: S_min = in.³

Below, fill in the missing portions of the beam shape designations for the most economical W10, W12, W14, W16, and W18 shapes that are acceptable for this case. Also, enter the corresponding section modulus for each case.^{^Answers:}

The most economical W10 shape is: W10 x	with S =	in.³
The most economical W12 shape is: W12 x	with S =	in.³
The most economical W14 shape is: W14 x	with S =	in.³
The most economical W16 shape is: W16 x	with S =	in.³
The most economical W18 shape is: W18 x	with S =	in.³

Choose the most economical W shape for this beam. Select only from the W10, W12, W14, W16, and W18 shapes that were considered in Part 4. If you have more than one choice with the same weight, choose the shorter shape.

Answer: The most economical shape has a weight of lb/ft

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