Applied Statics and Strength of Materials (6th Edition)
6th Edition
ISBN: 9780133840544
Author: George F. Limbrunner, Craig D'Allaird, Leonard Spiegel
Publisher: PEARSON
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Chapter 14, Problem 14.31SP
A timber beam is subjected to a maximum bending moment of
(a) Calculate the maximum bending stress.
(b) Calculate the bending stress
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Consider an 8-m long simply supported T-beam with overhangs loaded as shown below.
200 mm
w kN/m
50 mm
50 kN-m
50 kN-m
200 mm
2 m
4 m
2 m
50 mm
1.
Determine the location of the neutral axis measured from the top of
the beam and the moment of inertia (in mm4) of the section about its
neutral axis.
Draw the shear and bending moment diagrams. Annotate all relevant
values and distances. Determine the magnitude of the maximum negative
2.
moment.
Determine the minimum allowable strength of the beam in tension
and the minimum allowable strength of the beam in compression.
3.
Determine the maximum allowable load, w (in kN/m), that can be
applied pn the beam.
4.
B.
For certain values of w and P, the maximum positive bending moment in the beam is +8840 lb-ft, and the maximum negative bending
moment is-10336 lb-ft. The cross section of the beam is shown. The pertinent section properties of the cross section are e = 4.65 in..f
-3.05 in, and I, - 13.7725 in.. Calculate (a) the maximum tensile bending stress and (b) the maximum compressive bending stress
that is produced in the beam. Enter your answers with the appropriate sign.
A
Answer:
Of=
gc
d
B
b
tik
psi
psi
C
D
An A-36 steel beam of following cross section is part of a bridge and it is subjected
loading as shown.
mmmmm
35 ft
250 lb/ft
10 in
35 ft
50 ft
25 in
600 lb/ft
*
Assume that the bridge has a self-weight of 250 lb/ft and due to the truck, the loading is
now 600 lb/ft for the 50 feet section as shown in the picture above. Now if the maximum
bending moment due to the truck is 865.625 kip-ft, that translates to a maximum bending
stress as shown in the table below.
25 in
50 ft
35 ft
Maximum Bending
stress (kpsi)
Cross-sectional shape Yield strength of steel Moment of inertia
of beam
A-36
9.97 kpsi
Rectangular
I-shaped Beam
36 kpsi
36 kpsi
21.633 kpsi
The cross-sectional dimensions of both shapes are shown below.
250 lb/ft
10 in
35 ft
(in)
13020
6290
Consider yourself as an engineer assigned to this bridge construction and discuss the
suitable options for the optimal cross-section of the bridge. Note that from the data
shown in the table, both rectangular and I-beam cross-sections have…
Chapter 14 Solutions
Applied Statics and Strength of Materials (6th Edition)
Ch. 14 - Calculate the section modulus for: (a) a 6 -in-by-...Ch. 14 - Calculate the section modulus (with respect to the...Ch. 14 - Prob. 14.3PCh. 14 - Rework Problem 14.3 changing the orientation of...Ch. 14 - Assume that the timber member (a) of Problem 14.2...Ch. 14 - The structural steel built-up member (b) of...Ch. 14 - A round steel rod, 25 mm in diameter, is subjected...Ch. 14 - A square steel bar, 38 mm on each side, is used as...Ch. 14 - Calculate the moment strength for a W36302...Ch. 14 - Calculate the allowable bending moment for a solid...
Ch. 14 - The beams of cross sections shown are subjected to...Ch. 14 - A solid rectangular simply supported timber beam 6...Ch. 14 - A W1430 supports the loads shown. Calculate the...Ch. 14 - If the allowable shear stress is 100 MPa,...Ch. 14 - A steel pin 112 in diameter is subjected to a...Ch. 14 - A timber power-line pole is 10 in. in diameter at...Ch. 14 - Calculate the value of S and Z and the shape...Ch. 14 - For beams that have cross sections as shown for...Ch. 14 - Calculate the maximum load P that the beam shown...Ch. 14 - A 412 (S4S) hem-fir timber beam carries a...Ch. 14 - A simply supported W1636 A992 steel beam carries a...Ch. 14 - A W250115 steel wide-flange section supports a...Ch. 14 - Assume that the floor joist dimensions of Example...Ch. 14 - Calculate the allowable superimposed uniformly...Ch. 14 - A 3 -in.-by- 12 -in. (S4S) scaffold timber plank...Ch. 14 - For the following computer problems, any...Ch. 14 - For the following computer problems, any...Ch. 14 - For the following computer problems, any...Ch. 14 - Calculate the section modulus with respect to the...Ch. 14 - The timber box section (a) of Problem 14.29 is...Ch. 14 - A timber beam is subjected to a maximum bending...Ch. 14 - Rework Problem 14.31 assuming that the beam is...Ch. 14 - A 12 -in.-diameter steel rod projects 2 ft...Ch. 14 - Calculate the maximum bending stress in a W530101...Ch. 14 - A cantilever cast-iron beam is 6 ft long and has a...Ch. 14 - 14.36 Calculate the moment strength for a...Ch. 14 - A W813 steel wide-flange beam on a 20 -ft span is...Ch. 14 - A simply supported beam with a cruciform cross...Ch. 14 - A rectangular beam 100 mm in width and 250 mm in...Ch. 14 - The timber box section (a) of Problem 14.29 is...Ch. 14 - For the I-shaped timber beam shown, calculate the...Ch. 14 - 14.42 A steel wide-flange beam is oriented so that...Ch. 14 - A W1045steel wide-flange beam supports a uniformly...Ch. 14 - 14.44 A steel wide-flange section is subjected to...Ch. 14 - A W30108 steel wide-flange beam is simply...Ch. 14 - A W612 is strengthened with a 34 -in.-by- 34 -in....Ch. 14 - Four wood boards 1 in. by 6 in. in cross section...Ch. 14 - A lintel consists of two 8 -in.-by- 12 in. steel...Ch. 14 - A 50 -mm-by- 300 -mm scaffold timber plank, placed...Ch. 14 - A laminated wood beam is built up by gluing...Ch. 14 - A rectangular hollow shape carries loads as shown....Ch. 14 - For the beam shown, calculate the maximum tensile...Ch. 14 - 14.53 A box beam is built up of four -in.-by--in....Ch. 14 - 14.54 Find the value of the loads P that can be...Ch. 14 - 14.55 Solve Problem 14.54 assuming that the timber...Ch. 14 - Calculate the values of S and Z and the shape...Ch. 14 - 14.57 A is supported on simple supports on a -ft...
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- The cross-sectional dimensions of a beam are shown. Assume b=3.625 in., tetw=0.1875 in. and d=4.125 in. (a) If the bending stress at point K is 2470 psi (T), determine the internal bending moment M, acting about the z centroidal axis of the beam. (b) Determine the bending stress oy at point H (positive if tension, negative if compression). K d H Answers: (a) M2 = i Ib-ft. (b) oH = i psi.arrow_forwardThe cross-sectional dimensions of a beam are shown. Assume b-2.125 in., tt-0.3125 in. and d=2.125 in. (a) If the bending stress at point K is 3360 psi (T), determine the internal bending moment M₂ acting about the z centroidal axis of the beam. (b) Determine the bending stress o, at point H (positive if tension, negative if compression). H N K Answers: bf (a) M₂ = i (b) σH = i d lb-ft. psi.arrow_forwardThe cross-sectional dimensions of the beam are a = 4.8 in, b = 6.5 in, d=4.5 in, and t= 0.30 in. The internal bending moment about the z centroidal axis is Mz= -3.90 kip-ft. Answers both in psiarrow_forward
- A rectangular bar having width twice the depth is used as a beam. The beam is made of mild steel material having elastic modulus of 2.1 x 105 N/mm? and it undergoes bending by external load which makes radius of curvature of 150 m. If the allowable bending stress in the beam is to be limited to 100 MN/m. find the cross section of the beam.arrow_forwardThe simply supported beam is subjected to the loading and has cross-sectional area as in the figure below. Determine the absolute maximum bending stress in the beam at x = 4.5 ft. Neglect the weight of the beam. y 0.3 in. 360 lb/ft 3 in. 0.25 in. 3 in. |A FB | 0.3 in. 6 ft 3 ft 3 in. 3 in.arrow_forwardDraw the shear force and bending moment diagrams for the beam with loading shown below, P= 16 kN, w= 30 kN/m, M=40 kN.m. Also, state the maxmium shear force and bending moment in the text box. (Upload the diagrams showing all key values with units as well as neat and clear calculations) P kN P kN w kN/m M KN.m A 0.5 m 1 m 1 m- 1 m- -1 marrow_forward
- A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is (correct to one decimal place) 10 kN/m 4 marrow_forwardsimply supported beam in Fig. (b) has a rectangular cross section 120 mm wide and 200 mm high. (a) Draw and calculate the sheer force and bending moment diagrams for given simply supported beams. (b) Compute the maximum bending stress in the beams and sketch the bending stress distribution over the cross section on which the maximum bending stress occurs.arrow_forwardA beam is subjected to a negative bending moment of 8 kN-m. The cross-sectional dimensions of the beam are shown in Figure. Determine the bending stress at point H. Include a negative sign if compression. (in MPa.) Determine the moment of inertia about the centroidal x – axis (in mm4). Determine the maximum bending stress produced in the cross section. Include a negative sign if compression (in MPa). Determine the centroid location of the cross-section from the bottom fiber of the section (in mm). varrow_forward
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