This question about : Finding Maximum Normal stress in beams Please give me the

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This question about : Finding Maximum Normal stress in beams

Please give me the reason of question asked in the figure .

Principal Stress at Point b. The maximum principal slress at poirnt b in the critical section where M is maximum should not exceed 20 kips al,-21 ksi. Referring to Fig. 3, we write 3.2 kips/f Mmax 2873 kip-in Draw Mohr's circle (Fig. 4) and find T22.6ksi 127 in (.6ksi)9.88 in. 122 kips 1.45 ks 213ks(145k 21.3 ksi - 21.3 ksi + (1.45 ksi)2 41 kips 59 kips Conservatively, Tb max-21.4 ksi 24 ksi (OK) 11 ft 5 ft i V 41 kips -0.615 in. _ 1.45 ksi 34 12.2k pN 103 i. 21.3 ks -7.8 kips 279.4) 10) 0.88 in. b-21.3 ksi -43 kips Fig. 3 Key stress analysis lacations and normal stress distribution How to know that the normal stress is inward or outward? Tb-1.45 ksi 40 kip 239.4 kip ft Fig. 1 Free-body diagram of beam; shear and bending moment diagrams. an How to know that the shear stress is clockwise or counterclockwise? omar = 21.4 ksi Fig. 4 Stress element at point b and Mohr's circle for point b.

Explanation / Answer

1) If the bending moment is positive then the bending is called sagging bending moment. In this case all the points above the neutral axis (the horizontal line in the cross section shown in the above figure) are subjected to compressive normal stress(i.e inward) and all the points below the neutral axis are sujected to tensile normal stress(i.e outward).

If the bending moment is negative then the bending is called hogging bending moment. In this case all the points above the neutral axis are subjected to tensile normal stress(i.e outward) and all the points below the neutral axis are sujected to compressive normal stress(i.e inward).

In the question since the maximum bending moment is positive, all the points above the neutral axis are subjected to compression and all the points below the neutral axis are subjected to tension.

2)shear stress is in clockwise direction if shear force is positive and counter clockwise if the shear force is negative.

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