Cut a cross-section through the beam at any point and draw a free body diagram to the right of your cut. Determine the internal bending moment M(x). The diagram shows M(x) in its positive direction. Your answer may be negative. Check your equation by solving for M at x = 2.8 m. Wo M(x) L-x

Cut a cross-section through the beam at any point and draw a free body diagram to the right of your cut. Determine the internal bending moment M(x). The diagram shows M(x) in its positive direction. Your answer may be negative. Check your equation by solving for M at x = 2.8 m. Wo M(x) L-x

Mechanics of Materials (MindTap Course List)

9th Edition

ISBN:9781337093347

Author:Barry J. Goodno, James M. Gere

Publisher:Barry J. Goodno, James M. Gere

Chapter6: Stresses In Beams (advanced Topics)

Section: Chapter Questions

Problem 6.10.1P: Determine the shape factor f for a cross section in the shape of a double trapezoid having the...

See similar textbooks

Similar questions

Determine the shape factor f for a cross section in the shape of a double trapezoid having the dimensions shown in the figure. Also, check your result for the special cases of a rhombus (b1= 0) and a rectangle (b1= b2).
The simply supported beam is subjected to the force F = 700 N and the uniform distributed load with intensity w = 150 N/m. Draw the shear force and bending moment diagrams (in your homework documentation) and determine the equations for V(r) and M(x). Take a = 0 at point A. 19 F a Values for dimensions on the figure are given in the following table. Note the figure may not be to scale. Variable Value a 5.2 m 2.6 m 3.12 m Support Reactions The reaction at A is N. The reaction at D is N. Shear Force and Bending Moment Equations In section AB: V(x)= N and M(x)= N-m. In section BC: v(x)- N and M(x)= N-m. In section CD: V(x)- N and M(x)= N-m. A
3 For the beam shown, find the reactions at the supports and plot the shear-force and bending-moment diagrams. V = 9 kN, V2 = 9 kN, V3 = 200 mm, and V4 = 1100 mm. ATAT-V3 Provide values at all key points shown in the given shear-force and bending-moment diagrams. X (mm) B A = B = C = D = E= F= P = Q = E * KN * KN * KN × KN KN x KN ✩ kN.mm *kN.mm D 0.00 Reaction force R₁ (left) = In the shear-force and bending-moment diagrams given, +V 0.00 X (mm) 6.3 kN and reaction force R2 (right) = P 11.7 kN. Q 0.00
QUESTION 3 If the allowable bending stresses for a beam in one application is 6 kip/in2 in tension. The cross-section of the beam is W8 x 40. If the beam is 10 foot long and simply supported and has a concentrated load applied at x = 3 ft as shown below. • Generate the shear force and bending moment diagram in terms of P; • Based on the allowable maximum bending moment you just obtained above, calculate/ input the mazimm allowable value of the load P: please, pay attention to units, and calculate your answer to 1 decimal place.. 3 ft 7 ft kip.
1. Calculate reactions at the external supports. 2. Draw the free body diagram. 3. Build the diagrams if shear force and bending moment. (use the section method) 4. Find the diameter of section of the beam. 5. Calculate the maximum Tangential Stress and show the corresponding section. 6. Draw the stress distribution diagram in the most dangerous section of the beam. a (m) 4 b (m) | P (kN) q (kN/m) 1 80 8 A D-? [G] - 100 MPa a q B b P
A beam is supported and loaded as shown. In the section of the beam between 'A' and 'B', the equation for the resisting bending moment was determined as: M₁ = -6.5x²+50x. Determine the magnitude of maximum resisting bending moment (Mr,max) in the section. Note: Do NOT include units in your answer Answer: AA B
For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=11.0 ft, b-4.5 ft, c= 7.5 ft, w = 4 kips/ft and M = 250 kip-ft. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. 27 W Ay a b Calculate the reaction forces Ay and Cy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) W M a B M C b C C₂ C -X
Use the graphical method to construct the shear-force and bending-moment diagrams for the beam shown. Let a=4.0 ft, b=8.0 ft, c=4.0 ft, d=3.0 ft, w = 6.5 kips/ft and P = 45 kips. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. a B a W B W C b d For this loading, calculate the reaction forces Ay and Ey acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) b C C P C D P Ľ E d E ·x Ey
For the simply supported beam subjected to the loading shown, derive equations for the shear force Vand the bending moment M for any location in the beam. (Place the origin at point A.) Let a=2.50 m, b=4.25 m, PB = 45kN, and Pc = 90kN. Construct the shear- force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise. Answers: Ay = Dy= Mi i B Calculate the reaction forces Ay and Dy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) PB a PB B a Pc a Pc C kN b KN b D X D₂ X
10 in 1 in 1 in V 12 in 1 in 10 in The wide flange beam above is subjected to a vertical internal shear force V, as shown. Note that the diagram is not shown to scale. Which of the following is closest to the moment of inertia (I) that would be used to calculate the shear stresses on the cross-section due to V? 1051 in4 O 777 in4 O 991 in4 805 in4
For the simply supported beam subjected to the loading shown, derive equations for the shear force V and the bending moment M for any location in the beam. (Place the origin at point A.) Let a=12.0 ft, b=6.5 ft, c= 7.0 ft, w = 7 kips/ft and M = 230 kip-ft. Construct the shear-force and bending-moment diagrams on paper and use the results to answer the questions in the subsequent parts of this GO exercise.Calculate the reaction forces Ay and Cy acting on the beam. Positive values for the reactions are indicated by the directions of the red arrows shown on the free-body diagram below. (Note: Since Ax = 0, it has been omitted from the free-body diagram.) Determine the shear force acting at each of the following locations:(a) x = 0+ ft (i.e., just to the right of support A)(b) x = 12.0 ft (i,e., at point B)(c) x = 18.5- ft (i.e., just to the left of the support C)(d) x = 18.5+ ft (i.e., just to the right of the support (C)(e) x = 24.5 ftNote that x = 0 at support A. Determine the bending…
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.