A beam is subjected to a single vertical force at mid-span as shown. (Hint: the maximumbending moment occurs at mid-span of the beam)(a) Calculate the maximum bending stress in the beam considering a W16x77 sectionbending about its strong axis (see M9 Handout).(b) Calculate the maximum bending stress in the beam if the beam has a rectangular crosssection which is 16.5” in depth and 10.3” wide.(c) Calculate the % change in the maximum bending stress from the W16x77 section to therectangular section (part a and b). Also, calculate the % change in the in the crosssectional area from the W16x77 section to the rectangular section. Note whether eachchange is an increase or decrease. P4: A beam is subjected to a single vertical force at mid-span as shown. (Hint: the maximumbending moment occurs at mid-span of the beam)(a) Calculate the maximum bending stress in the beam considering a W16x77 sectionbending about its strong axis (see M9 Handout).(b) Calculate the maximum bending stress in the beam if the beam has a rectangular cross-section which is 16.5" in depth and 10.3" wide.(c) Calculate the % change in the maximum bending stress from the W16x77 section to therectangular section (part a and b). Also, calculate the % change in the in the cross-sectional area from the W16x77 section to the rectangular section. Note whether eachchange is an increase or decrease.24 kipfor12'12'

Maximum bending moment for beam under central load,Mmax = WL4 = 24×244 = 144 kip.ftFor W 16×77 section, Section modulus about strong axis(zx) =134 in.3 W 16×77, zx = Ixy = 134 in3 Using flexural formula ,MmaxIx = σmaxy Mmax = σmax. zxwhere, Mmax = Maximum bending moment = 144×12 = 1728 kip.inσmax = Maximum bending stressIx = Moment of inertia about strong axisy = Distance between Neutral axis to extreme part of elementHence, σmax = Mmaxzx = 1728134σmax = 12.895 kip/in.2Ix = bd312 = 10.3×16.5312 = 3855.741 in.4y = d2 = 16.52 = 8.25 in.Using flexural formula,MIx = σy17283855.741 = σmax8.25σmax = 3.70 kip/in.2% change = Final value - Initial valueInitial value×100% change in σmax = σmaxrect - σmaxW 16x77 σmaxW 16x77×100= 3.70 - 12.89512.895×100= - 71.31 %Cross -sectional Area of rectangle = b×d = 10.3×16.5 = 169.95 in.2Cross -sectional Area of W 16×77 = 22.6 in.2% change in cross-sectional area = Arect - AW 16x77AW 16x77×100= 169.95 - 22.622.6×100=+ 652%σmax fo W 16×77 = 12.895 kip/in2σmax for rectangle = 3.70 kip/in2% change in σmax = - 71.31 %% change in Area = + 652 %

Answered: A beam is subjected to a single…

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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A beam is subjected to a single vertical force at mid-span as shown. (Hint: the maximum
bending moment occurs at mid-span of the beam)
(a) Calculate the maximum bending stress in the beam considering a W16x77 section
bending about its strong axis (see M9 Handout).
(b) Calculate the maximum bending stress in the beam if the beam has a rectangular crosssection which is 16.5” in depth and 10.3” wide.
(c) Calculate the % change in the maximum bending stress from the W16x77 section to the
rectangular section (part a and b). Also, calculate the % change in the in the crosssectional area from the W16x77 section to the rectangular section. Note whether each
change is an increase or decrease.

P4: A beam is subjected to a single vertical force at mid-span as shown. (Hint: the maximum
bending moment occurs at mid-span of the beam)
(a) Calculate the maximum bending stress in the beam considering a W16x77 section
bending about its strong axis (see M9 Handout).
(b) Calculate the maximum bending stress in the beam if the beam has a rectangular cross-
section which is 16.5" in depth and 10.3" wide.
(c) Calculate the % change in the maximum bending stress from the W16x77 section to the
rectangular section (part a and b). Also, calculate the % change in the in the cross-
sectional area from the W16x77 section to the rectangular section. Note whether each
change is an increase or decrease.
24 kip
for
12'
12'

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